EMA-Stichprobenvergleiche (d = 0.88) für n = 100

1.1 Drawing a Random Sample of n = 100

# or with slice_sample(n = 100)
rand = sample(EMA_5.5$ID, size = 100)

EMA_5.5 = EMA_5.5 %>% 
  filter(ID %in% rand)

EMA_30.30 = EMA_30.30 %>%
  filter(ID %in% rand)

EMA_5.5_Window = EMA_5.5_Window %>%
  filter(ID %in% rand)

EMA_5.5_Days = EMA_5.5_Days %>%
  filter(ID %in% rand)

1.2 Überblick über die simulierten Daten

Beispiel-Verläufe in den 4 untersuchten Datensets

1.2.1 Original-Simulationsdaten (je 5 MZP)

EMA_5.5 %>%
  within(., {ind.pretestSD = round(ind.pretestSD, digits = 2)
            ind.posttestSD = round(ind.posttestSD, digits = 2)}) %>% 
  head() %>% 
  kable() %>% 
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE) %>% 
  scroll_box(width = "100%")

ID	ID_orig	PRE1_1	PRE1_2	PRE1_3	PRE1_4	PRE1_5	POST1_1	POST1_2	POST1_3	POST1_4	POST1_5	PRE_Mean	POST_Mean	MeanDiff	ind.pretestSD	ind.posttestSD
16	17	13	9	13	11	9	10	5	9	9	13	11.0	9.2	1.8	2.00	2.86
33	37	8	8	7	0	12	4	1	5	6	8	7.0	4.8	2.2	4.36	2.59
82	91	12	10	13	9	10	10	5	3	5	8	10.8	6.2	4.6	1.64	2.77
103	118	14	11	11	11	10	15	7	7	9	6	11.4	8.8	2.6	1.52	3.63
259	299	6	6	6	7	11	15	12	5	9	9	7.2	10.0	-2.8	2.17	3.74
299	342	18	14	13	7	9	16	13	10	4	7	12.2	10.0	2.2	4.32	4.74

Pre-Post-Verläufe für 9 zufällig gezogene Personen

rand = sample(EMA_5.5$ID, 9)

x = tibble(ID = c(rep(rand[1],times=11),
                  rep(rand[2],times=11),
                  rep(rand[3],times=11),
                  rep(rand[4],times=11),
                  rep(rand[5],times=11),
                  rep(rand[6],times=11),
                  rep(rand[7],times=11),
                  rep(rand[8],times=11),
                  rep(rand[9],times=11)),
           MZP = rep(seq(as.Date("2020-01-01"), length.out=11, by="1 day"), times=9),
           Score = c(as.numeric(EMA_5.5[rand[1],pre_5mzp]), NA, as.numeric(EMA_5.5[rand[1],post_5mzp]),
                     as.numeric(EMA_5.5[rand[2],pre_5mzp]), NA, as.numeric(EMA_5.5[rand[2],post_5mzp]),
                     as.numeric(EMA_5.5[rand[3],pre_5mzp]), NA, as.numeric(EMA_5.5[rand[3],post_5mzp]),
                     as.numeric(EMA_5.5[rand[4],pre_5mzp]), NA, as.numeric(EMA_5.5[rand[4],post_5mzp]),
                     as.numeric(EMA_5.5[rand[5],pre_5mzp]), NA, as.numeric(EMA_5.5[rand[5],post_5mzp]),
                     as.numeric(EMA_5.5[rand[6],pre_5mzp]), NA, as.numeric(EMA_5.5[rand[6],post_5mzp]),
                     as.numeric(EMA_5.5[rand[7],pre_5mzp]), NA, as.numeric(EMA_5.5[rand[7],post_5mzp]),
                     as.numeric(EMA_5.5[rand[8],pre_5mzp]), NA, as.numeric(EMA_5.5[rand[8],post_5mzp]),
                     as.numeric(EMA_5.5[rand[9],pre_5mzp]), NA, as.numeric(EMA_5.5[rand[9],post_5mzp])))

x %>%
  group_by(ID) %>% 
  plot_time_series(MZP, Score,
    #.color_var = ID,           # for multiple lines in one plot
    #.color_lab = "ID",
    .facet_ncol = 3,
    .facet_scales = "fixed",
    .interactive = TRUE,
    .facet_collapse = FALSE,
    .smooth = TRUE,
    .smooth_degree = 2,
    .smooth_alpha = 0.5,
    .smooth_size = 0.2
  )

# don´t run this section (code for extremely computation-intense plots that I already stored as .RData and .jpg)
# repeated-measures scatter-boxplot-violin-histograms for individual PRE and POST means
# from van Langen (2020) Open-visualizations tutorial for repeated measures in R

# EMA_5.5
# converting my dataframes to use in the same ggplot structure:
EMA_5.5_ts = EMA_5.5 %>% 
  select(ID, PRE_Mean, POST_Mean) %>% 
  pivot_longer(!ID, names_to = "Interval", values_to = "Mean") %>% 
  mutate(ID = as.factor(ID),
         Interval = rep(c(1,2), times = nrow(EMA_5.5)))

save(EMA_5.5_ts, file = "Time Series Dataframes/k20_EMA_5.5_n100_ts.RData")

###

load("Time Series Dataframes/k20_EMA_5.5_n100_ts.RData")

# Repeated measures with box− and violin plots
EMA_5.5_ts$jit = jitter(EMA_5.5_ts$Interval, amount = .09)

Pre_Post_Box_Violin = ggplot(data = EMA_5.5_ts, aes(y = Mean)) +
  geom_point(data = EMA_5.5_ts %>% filter(Interval == "1"), aes(x = jit), color = "dodgerblue", size = 1,
             alpha = .5) +
  geom_point(data = EMA_5.5_ts %>% filter(Interval == "2"), aes(x = jit), color = "darkorange", size = 1,
             alpha = .5) +
  geom_line(aes(x = jit, group = ID), color = "lightgray", alpha = .05) +
  geom_half_boxplot(
    data = EMA_5.5_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.25),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = TRUE, width = .1,
    fill = "dodgerblue", alpha = .5) +
  geom_half_boxplot(
    data = EMA_5.5_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .15),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = TRUE, width = .1,
    fill = "darkorange", alpha = .5) +
  geom_half_violin(
    data = EMA_5.5_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = 1.3),
    side = "r", fill = "dodgerblue", alpha = .5, trim = FALSE) +
  geom_half_violin(
    data = EMA_5.5_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .3),
    side = "r", fill = "darkorange", alpha = .5, trim = FALSE) +
  scale_x_continuous(breaks = c(1,2), labels = c("PRE", "POST"), limits = c(0, 3)) +
  xlab("Interval") + ylab("PHQ-9 Mean Score") +
  #ggtitle("EMA Data (5+5 Timepoints): Individual Pre-Post Means") +
  #theme_classic() +
  theme_bw() +
  coord_cartesian(ylim = c(0, 24))

ggsave("Time Series Dataframes/k20_EMA_5.5_n100_Pre-Post_Box_Violin.jpg", plot = Pre_Post_Box_Violin, width = 6, height = 4)
save(Pre_Post_Box_Violin, file = "Time Series Dataframes/k20_EMA_5.5_n100_Pre_Post_Box_Violin.RData")


# Repeated measures with box− and violin plots and means + CIs
score_mean_1 = EMA_5.5_ts %>% filter(Interval == "1") %>% summarise(mean(Mean)) %>% as.numeric()
score_mean_2 = EMA_5.5_ts %>% filter(Interval == "2") %>% summarise(mean(Mean)) %>% as.numeric()
score_median1 = EMA_5.5_ts %>% filter(Interval == "1") %>% summarise(median(Mean)) %>% as.numeric()
score_median2 = EMA_5.5_ts %>% filter(Interval == "2") %>% summarise(median(Mean)) %>% as.numeric()
score_sd_1 = EMA_5.5_ts %>% filter(Interval == "1") %>% summarise(sd(Mean)) %>% as.numeric()
score_sd_2 = EMA_5.5_ts %>% filter(Interval == "2") %>% summarise(sd(Mean)) %>% as.numeric()
score_se_1 = score_sd_1/sqrt(nrow(EMA_5.5))
score_se_2 = score_sd_2/sqrt(nrow(EMA_5.5))
score_ci_1 = EMA_5.5_ts %>% filter(Interval == "1") %>% pull(Mean) %>% CI(., ci = 0.95)
score_ci_2 = EMA_5.5_ts %>% filter(Interval == "2") %>% pull(Mean) %>% CI(., ci = 0.95)
#Create data frame with 2 rows and 7 columns containing the descriptives
group = c("PRE", "POST")
N = c(nrow(EMA_5.5), nrow(EMA_5.5))
score_mean = c(score_mean_1, score_mean_2)
score_median = c(score_median1, score_median2)
sd = c(score_sd_1, score_sd_2)
se = c(score_se_1, score_se_2)
ci = c(as.numeric(score_ci_1[1] - score_ci_1[3]), as.numeric(score_ci_2[1] - score_ci_2[3]))
summary_df = data.frame(group, N, score_mean, score_median, sd, se, ci)

# EMA_5.5_ts$jit = jitter(EMA_5.5_ts$Interval, amount = .09)     #already created above
x_tick_means = c(.87, 2.13)

Pre_Post_Box_Violin_Mean_CI = ggplot(data = EMA_5.5_ts, aes(y = Mean)) +
  geom_point(data = EMA_5.5_ts %>% filter(Interval == "1"), aes(x = jit), color = "dodgerblue", size = 1,
             alpha = .6) +
  geom_point(data = EMA_5.5_ts %>% filter(Interval == "2"), aes(x = jit), color = "darkorange", size = 1,
             alpha = .6) +
  geom_line(aes(x = jit, group = ID), color = "lightgray", alpha = .05) +
  geom_half_boxplot(
    data = EMA_5.5_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.28),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = FALSE, width = .2,
    fill = "dodgerblue") +
  geom_half_boxplot(
    data = EMA_5.5_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .18),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = FALSE, width = .2,
    fill = "darkorange") +
  geom_half_violin(
    data = EMA_5.5_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.3),
    side = "l", fill = "dodgerblue") +
  geom_half_violin(
    data = EMA_5.5_ts %>% filter(Interval == "2"),aes(x = Interval, y = Mean), position = position_nudge(x = .3),
    side = "r", fill = "darkorange") +
  geom_point(data = EMA_5.5_ts %>% filter(Interval == "1"), aes(x = Interval, y = score_mean[1]),
             position = position_nudge(x = -.13), color = "dodgerblue", alpha = .6, size = 1.5) +
  geom_errorbar(data = EMA_5.5_ts %>% filter(Interval == "1"), aes(x = Interval, y = score_mean[1],
                                                 ymin = score_mean[1]-ci[1], ymax = score_mean[1]+ci[1]),
                position = position_nudge(-.13), color = "dodgerblue", width = 0.05, size = 0.4, alpha = .6) +
  geom_point(data = EMA_5.5_ts %>% filter(Interval == "2"), aes(x = Interval, y = score_mean[2]),
             position = position_nudge(x = .13), color = "darkorange", alpha = .6, size = 1.5)+
  geom_errorbar(data = EMA_5.5_ts %>% filter(Interval == "2"), aes(x = Interval, y = score_mean[2],
                                                 ymin = score_mean[2]-ci[2], ymax = score_mean[2]+ci[2]), 
                position = position_nudge(.13), color = "darkorange", width = 0.05, size = 0.4, alpha = .6) +
  geom_line(data = summary_df, aes(x = x_tick_means, y = score_mean), color = "gray", size = 1) +
  scale_x_continuous(breaks = c(1,2), labels = c("PRE", "POST"), limits = c(0, 3)) +
  xlab("Interval") + ylab("PHQ-9 Mean Score") +
  #ggtitle("EMA Data (5+5 Timepoints): Individual Pre-Post Means") +
  #theme_classic() +
  theme_bw() +
  coord_cartesian(ylim = c(0, 24))

ggsave("Time Series Dataframes/k20_EMA_5.5_n100_Pre-Post_Box_Violin_Mean+CI.jpg", plot = Pre_Post_Box_Violin_Mean_CI, width = 6, height = 4)
save(Pre_Post_Box_Violin_Mean_CI, file = "Time Series Dataframes/k20_EMA_5.5_n100_Pre_Post_Box_Violin_Mean_CI.RData")

#knitr::include_graphics("Time Series Dataframes/k20_EMA_5.5_n100_Pre-Post_Box_Violin.jpg")
knitr::include_graphics("Time Series Dataframes/k20_EMA_5.5_n100_Pre-Post_Box_Violin_Mean+CI.jpg")

1.2.2 Erweiterte Intervall-Daten (je 30 MZP)

EMA_30.30 %>% 
  select(-(ID1_PRE:ID6_POST)) %>% 
  within(., {ind.pretestSD = round(ind.pretestSD, digits = 2)
            ind.posttestSD = round(ind.posttestSD, digits = 2)}) %>% 
  head() %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE) %>% 
  scroll_box(width = "100%")

ID	PRE1_1	PRE1_2	PRE1_3	PRE1_4	PRE1_5	PRE1_6	PRE1_7	PRE1_8	PRE1_9	PRE1_10	PRE1_11	PRE1_12	PRE1_13	PRE1_14	PRE1_15	PRE1_16	PRE1_17	PRE1_18	PRE1_19	PRE1_20	PRE1_21	PRE1_22	PRE1_23	PRE1_24	PRE1_25	PRE1_26	PRE1_27	PRE1_28	PRE1_29	PRE1_30	POST1_1	POST1_2	POST1_3	POST1_4	POST1_5	POST1_6	POST1_7	POST1_8	POST1_9	POST1_10	POST1_11	POST1_12	POST1_13	POST1_14	POST1_15	POST1_16	POST1_17	POST1_18	POST1_19	POST1_20	POST1_21	POST1_22	POST1_23	POST1_24	POST1_25	POST1_26	POST1_27	POST1_28	POST1_29	POST1_30	PRE_Mean	POST_Mean	MeanDiff	ind.pretestSD	ind.posttestSD
16	13	9	13	11	9	10	12	13	12	8	13	13	9	11	9	12	9	10	10	14	9	11	9	13	13	9	9	11	13	13	10	5	9	9	13	13	10	5	9	9	7	11	9	13	6	9	6	11	7	13	7	9	13	11	6	13	9	10	5	9	11.0	9.2	1.8	1.82	2.61
33	8	8	7	0	12	10	6	11	8	0	10	11	0	8	6	14	6	4	3	8	6	8	0	10	11	0	6	11	10	8	4	1	5	6	8	5	1	4	6	8	3	4	7	2	8	6	2	7	7	2	4	1	8	5	6	3	4	7	8	2	7.0	4.8	2.2	3.97	2.35
82	12	10	13	9	10	12	9	12	12	9	12	13	10	10	9	9	12	9	12	12	12	13	10	9	10	12	13	9	10	10	10	5	3	5	8	2	8	9	7	5	7	2	8	9	5	9	6	9	4	3	9	8	5	2	7	4	10	7	3	7	10.8	6.2	4.6	1.49	2.52
103	14	11	11	11	10	11	10	11	14	11	10	10	13	11	13	11	9	13	12	12	11	10	10	13	13	9	12	12	11	13	15	7	7	9	6	7	5	7	14	11	7	6	9	15	7	6	7	9	15	7	7	7	11	14	5	7	14	11	7	5	11.4	8.8	2.6	1.38	3.31
259	6	6	6	7	11	10	4	8	7	7	7	10	8	7	4	10	9	5	6	6	6	6	11	6	7	8	9	6	4	9	15	12	5	9	9	8	13	15	7	7	6	6	12	12	14	8	11	11	15	5	9	13	11	13	4	7	7	13	15	8	7.2	10.0	-2.8	1.97	3.40
299	18	14	13	7	9	9	9	10	14	19	15	15	8	7	16	18	13	11	13	6	18	13	14	7	9	14	19	10	9	9	16	13	10	4	7	15	12	13	6	4	6	18	9	10	7	10	8	4	17	11	14	11	10	13	2	10	3	9	12	16	12.2	10.0	2.2	3.93	4.32

Pre-Post-Verläufe für 9 zufällig gezogene Personen

rand = sample(EMA_30.30$ID, 9)

x = tibble(ID = c(rep(rand[1],times=61),
                     rep(rand[2],times=61),
                     rep(rand[3],times=61),
                     rep(rand[4],times=61),
                     rep(rand[5],times=61),
                     rep(rand[6],times=61),
                     rep(rand[7],times=61),
                     rep(rand[8],times=61),
                     rep(rand[9],times=61)),
              MZP = rep(seq(as.Date("2020-01-01"), length.out=61, by="1 day"), times=9),
              Score = c(as.numeric(EMA_30.30[rand[1],pre_30mzp]), NA, as.numeric(EMA_30.30[rand[1],post_30mzp]),
                        as.numeric(EMA_30.30[rand[2],pre_30mzp]), NA, as.numeric(EMA_30.30[rand[2],post_30mzp]),
                        as.numeric(EMA_30.30[rand[3],pre_30mzp]), NA, as.numeric(EMA_30.30[rand[3],post_30mzp]),
                        as.numeric(EMA_30.30[rand[4],pre_30mzp]), NA, as.numeric(EMA_30.30[rand[4],post_30mzp]),
                        as.numeric(EMA_30.30[rand[5],pre_30mzp]), NA, as.numeric(EMA_30.30[rand[5],post_30mzp]),
                        as.numeric(EMA_30.30[rand[6],pre_30mzp]), NA, as.numeric(EMA_30.30[rand[6],post_30mzp]),
                        as.numeric(EMA_30.30[rand[7],pre_30mzp]), NA, as.numeric(EMA_30.30[rand[7],post_30mzp]),
                        as.numeric(EMA_30.30[rand[8],pre_30mzp]), NA, as.numeric(EMA_30.30[rand[8],post_30mzp]),
                        as.numeric(EMA_30.30[rand[9],pre_30mzp]), NA, as.numeric(EMA_30.30[rand[9],post_30mzp])))

x %>%
  group_by(ID) %>% 
  plot_time_series(MZP, Score,
    #.color_var = ID,           # for multiple lines in one plot
    #.color_lab = "ID",
    .facet_ncol = 3,
    .facet_scales = "fixed",
    .interactive = TRUE,
    .facet_collapse = FALSE,
    .smooth = TRUE,
    .smooth_degree = 2,
    .smooth_alpha = 0.5,
    .smooth_size = 0.2
  )

# don´t run this section (code for extremely computation-intense plots that I already stored as .RData and .jpg)
# repeated-measures scatter-boxplot-violin-histograms for individual PRE and POST means
# from van Langen (2020) Open-visualizations tutorial for repeated measures in R

# EMA_30.30
# converting my dataframes to use in the same ggplot structure:
EMA_30.30_ts = EMA_30.30 %>% 
  select(ID, PRE_Mean, POST_Mean) %>% 
  pivot_longer(!ID, names_to = "Interval", values_to = "Mean") %>% 
  mutate(ID = as.factor(ID),
         Interval = rep(c(1,2), times = nrow(EMA_30.30)))

save(EMA_30.30_ts, file = "Time Series Dataframes/k20_EMA_30.30_n100_ts.RData")

###

load("Time Series Dataframes/k20_EMA_30.30_n100_ts.RData")

# Repeated measures with box− and violin plots
EMA_30.30_ts$jit = jitter(EMA_30.30_ts$Interval, amount = .09)

Pre_Post_Box_Violin = ggplot(data = EMA_30.30_ts, aes(y = Mean)) +
  geom_point(data = EMA_30.30_ts %>% filter(Interval == "1"), aes(x = jit), color = "dodgerblue", size = 1,
             alpha = .5) +
  geom_point(data = EMA_30.30_ts %>% filter(Interval == "2"), aes(x = jit), color = "darkorange", size = 1,
             alpha = .5) +
  geom_line(aes(x = jit, group = ID), color = "lightgray", alpha = .05) +
  geom_half_boxplot(
    data = EMA_30.30_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.25),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = TRUE, width = .1,
    fill = "dodgerblue", alpha = .5) +
  geom_half_boxplot(
    data = EMA_30.30_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .15),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = TRUE, width = .1,
    fill = "darkorange", alpha = .5) +
  geom_half_violin(
    data = EMA_30.30_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = 1.3),
    side = "r", fill = "dodgerblue", alpha = .5, trim = FALSE) +
  geom_half_violin(
    data = EMA_30.30_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .3),
    side = "r", fill = "darkorange", alpha = .5, trim = FALSE) +
  scale_x_continuous(breaks = c(1,2), labels = c("PRE", "POST"), limits = c(0, 3)) +
  xlab("Interval") + ylab("PHQ-9 Mean Score") +
  #ggtitle("EMA Data (30+30 Timepoints): Individual Pre-Post Means") +
  #theme_classic() +
  theme_bw() +
  coord_cartesian(ylim = c(0, 24))

ggsave("Time Series Dataframes/k20_EMA_30.30_n100_Pre-Post_Box_Violin.jpg", plot = Pre_Post_Box_Violin, width = 6, height = 4)
save(Pre_Post_Box_Violin, file = "Time Series Dataframes/k20_EMA_30.30_n100_Pre_Post_Box_Violin.RData")


# Repeated measures with box− and violin plots and means + CIs
score_mean_1 = EMA_30.30_ts %>% filter(Interval == "1") %>% summarise(mean(Mean)) %>% as.numeric()
score_mean_2 = EMA_30.30_ts %>% filter(Interval == "2") %>% summarise(mean(Mean)) %>% as.numeric()
score_median1 = EMA_30.30_ts %>% filter(Interval == "1") %>% summarise(median(Mean)) %>% as.numeric()
score_median2 = EMA_30.30_ts %>% filter(Interval == "2") %>% summarise(median(Mean)) %>% as.numeric()
score_sd_1 = EMA_30.30_ts %>% filter(Interval == "1") %>% summarise(sd(Mean)) %>% as.numeric()
score_sd_2 = EMA_30.30_ts %>% filter(Interval == "2") %>% summarise(sd(Mean)) %>% as.numeric()
score_se_1 = score_sd_1/sqrt(nrow(EMA_30.30))
score_se_2 = score_sd_2/sqrt(nrow(EMA_30.30))
score_ci_1 = EMA_30.30_ts %>% filter(Interval == "1") %>% pull(Mean) %>% CI(., ci = 0.95)
score_ci_2 = EMA_30.30_ts %>% filter(Interval == "2") %>% pull(Mean) %>% CI(., ci = 0.95)
#Create data frame with 2 rows and 7 columns containing the descriptives
group = c("PRE", "POST")
N = c(nrow(EMA_30.30), nrow(EMA_30.30))
score_mean = c(score_mean_1, score_mean_2)
score_median = c(score_median1, score_median2)
sd = c(score_sd_1, score_sd_2)
se = c(score_se_1, score_se_2)
ci = c(as.numeric(score_ci_1[1] - score_ci_1[3]), as.numeric(score_ci_2[1] - score_ci_2[3]))
summary_df = data.frame(group, N, score_mean, score_median, sd, se, ci)

# EMA_30.30_ts$jit = jitter(EMA_30.30_ts$Interval, amount = .09)     #already created above
x_tick_means = c(.87, 2.13)

Pre_Post_Box_Violin_Mean_CI = ggplot(data = EMA_30.30_ts, aes(y = Mean)) +
  geom_point(data = EMA_30.30_ts %>% filter(Interval == "1"), aes(x = jit), color = "dodgerblue", size = 1,
             alpha = .6) +
  geom_point(data = EMA_30.30_ts %>% filter(Interval == "2"), aes(x = jit), color = "darkorange", size = 1,
             alpha = .6) +
  geom_line(aes(x = jit, group = ID), color = "lightgray", alpha = .05) +
  geom_half_boxplot(
    data = EMA_30.30_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.28),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = FALSE, width = .2,
    fill = "dodgerblue") +
  geom_half_boxplot(
    data = EMA_30.30_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .18),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = FALSE, width = .2,
    fill = "darkorange") +
  geom_half_violin(
    data = EMA_30.30_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.3),
    side = "l", fill = "dodgerblue") +
  geom_half_violin(
    data = EMA_30.30_ts %>% filter(Interval == "2"),aes(x = Interval, y = Mean), position = position_nudge(x = .3),
    side = "r", fill = "darkorange") +
  geom_point(data = EMA_30.30_ts %>% filter(Interval == "1"), aes(x = Interval, y = score_mean[1]),
             position = position_nudge(x = -.13), color = "dodgerblue", alpha = .6, size = 1.5) +
  geom_errorbar(data = EMA_30.30_ts %>% filter(Interval == "1"), aes(x = Interval, y = score_mean[1],
                                                 ymin = score_mean[1]-ci[1], ymax = score_mean[1]+ci[1]),
                position = position_nudge(-.13), color = "dodgerblue", width = 0.05, size = 0.4, alpha = .6) +
  geom_point(data = EMA_30.30_ts %>% filter(Interval == "2"), aes(x = Interval, y = score_mean[2]),
             position = position_nudge(x = .13), color = "darkorange", alpha = .6, size = 1.5)+
  geom_errorbar(data = EMA_30.30_ts %>% filter(Interval == "2"), aes(x = Interval, y = score_mean[2],
                                                 ymin = score_mean[2]-ci[2], ymax = score_mean[2]+ci[2]), 
                position = position_nudge(.13), color = "darkorange", width = 0.05, size = 0.4, alpha = .6) +
  geom_line(data = summary_df, aes(x = x_tick_means, y = score_mean), color = "gray", size = 1) +
  scale_x_continuous(breaks = c(1,2), labels = c("PRE", "POST"), limits = c(0, 3)) +
  xlab("Interval") + ylab("PHQ-9 Mean Score") +
  #ggtitle("EMA Data (30+30 Timepoints): Individual Pre-Post Means") +
  #theme_classic() +
  theme_bw() +
  coord_cartesian(ylim = c(0, 24))

ggsave("Time Series Dataframes/k20_EMA_30.30_n100_Pre-Post_Box_Violin_Mean+CI.jpg", plot = Pre_Post_Box_Violin_Mean_CI, width = 6, height = 4)
save(Pre_Post_Box_Violin_Mean_CI, file = "Time Series Dataframes/k20_EMA_30.30_n100_Pre_Post_Box_Violin_Mean_CI.RData")

#knitr::include_graphics("Time Series Dataframes/k20_EMA_30.30_n100_Pre-Post_Box_Violin.jpg")
knitr::include_graphics("Time Series Dataframes/k20_EMA_30.30_n100_Pre-Post_Box_Violin_Mean+CI.jpg")

1.2.3 Zufallsauswahl: Random Window (je 5 MZP)

EMA_5.5_Window %>%
  within(., {ind.pretestSD = round(ind.pretestSD, digits = 2)
            ind.posttestSD = round(ind.posttestSD, digits = 2)}) %>% 
  head() %>% 
  kable() %>% 
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE) %>% 
  scroll_box(width = "100%")

ID	Pre_MZP1	Pre_MZP2	Pre_MZP3	Pre_MZP4	Pre_MZP5	Post_MZP1	Post_MZP2	Post_MZP3	Post_MZP4	Post_MZP5	PRE1_1	PRE1_2	PRE1_3	PRE1_4	PRE1_5	POST1_1	POST1_2	POST1_3	POST1_4	POST1_5	PRE_Mean	POST_Mean	MeanDiff	ind.pretestSD	ind.posttestSD
16	PRE1_1	PRE1_2	PRE1_3	PRE1_4	PRE1_5	POST1_10	POST1_11	POST1_12	POST1_13	POST1_14	13	9	13	11	9	9	7	11	9	13	11.0	9.8	1.2	2.00	2.28
33	PRE1_6	PRE1_7	PRE1_8	PRE1_9	PRE1_10	POST1_26	POST1_27	POST1_28	POST1_29	POST1_30	10	6	11	8	0	3	4	7	8	2	7.0	4.8	2.2	4.36	2.59
82	PRE1_12	PRE1_13	PRE1_14	PRE1_15	PRE1_16	POST1_26	POST1_27	POST1_28	POST1_29	POST1_30	13	10	10	9	9	4	10	7	3	7	10.2	6.2	4.0	1.64	2.77
103	PRE1_20	PRE1_21	PRE1_22	PRE1_23	PRE1_24	POST1_1	POST1_2	POST1_3	POST1_4	POST1_5	12	11	10	10	13	15	7	7	9	6	11.2	8.8	2.4	1.30	3.63
259	PRE1_2	PRE1_3	PRE1_4	PRE1_5	PRE1_6	POST1_7	POST1_8	POST1_9	POST1_10	POST1_11	6	6	7	11	10	13	15	7	7	6	8.0	9.6	-1.6	2.35	4.10
299	PRE1_17	PRE1_18	PRE1_19	PRE1_20	PRE1_21	POST1_26	POST1_27	POST1_28	POST1_29	POST1_30	13	11	13	6	18	10	3	9	12	16	12.2	10.0	2.2	4.32	4.74

Pre-Post-Verläufe für 9 zufällig gezogene Personen

rand = sample(EMA_5.5_Window$ID, 9)

x = tibble(ID = c(rep(rand[1],times=11),
                  rep(rand[2],times=11),
                  rep(rand[3],times=11),
                  rep(rand[4],times=11),
                  rep(rand[5],times=11),
                  rep(rand[6],times=11),
                  rep(rand[7],times=11),
                  rep(rand[8],times=11),
                  rep(rand[9],times=11)),
           MZP = rep(seq(as.Date("2020-01-01"), length.out=11, by="1 day"), times=9),
           Score = c(as.numeric(EMA_5.5_Window[rand[1],pre_5mzp]), NA, as.numeric(EMA_5.5_Window[rand[1],post_5mzp]),
                     as.numeric(EMA_5.5_Window[rand[2],pre_5mzp]), NA, as.numeric(EMA_5.5_Window[rand[2],post_5mzp]),
                     as.numeric(EMA_5.5_Window[rand[3],pre_5mzp]), NA, as.numeric(EMA_5.5_Window[rand[3],post_5mzp]),
                     as.numeric(EMA_5.5_Window[rand[4],pre_5mzp]), NA, as.numeric(EMA_5.5_Window[rand[4],post_5mzp]),
                     as.numeric(EMA_5.5_Window[rand[5],pre_5mzp]), NA, as.numeric(EMA_5.5_Window[rand[5],post_5mzp]),
                     as.numeric(EMA_5.5_Window[rand[6],pre_5mzp]), NA, as.numeric(EMA_5.5_Window[rand[6],post_5mzp]),
                     as.numeric(EMA_5.5_Window[rand[7],pre_5mzp]), NA, as.numeric(EMA_5.5_Window[rand[7],post_5mzp]),
                     as.numeric(EMA_5.5_Window[rand[8],pre_5mzp]), NA, as.numeric(EMA_5.5_Window[rand[8],post_5mzp]),
                     as.numeric(EMA_5.5_Window[rand[9],pre_5mzp]), NA, as.numeric(EMA_5.5_Window[rand[9],post_5mzp])))

x %>%
  group_by(ID) %>% 
  plot_time_series(MZP, Score,
    #.color_var = ID,           # for multiple lines in one plot
    #.color_lab = "ID",
    .facet_ncol = 3,
    .facet_scales = "fixed",
    .interactive = TRUE,
    .facet_collapse = FALSE,
    .smooth = TRUE,
    .smooth_degree = 2,
    .smooth_alpha = 0.5,
    .smooth_size = 0.2
  )

# don´t run this section (code for extremely computation-intense plots that I already stored as .RData and .jpg)
# repeated-measures scatter-boxplot-violin-histograms for individual PRE and POST means
# from van Langen (2020) Open-visualizations tutorial for repeated measures in R

# EMA_5.5_Window
# converting my dataframes to use in the same ggplot structure:
EMA_5.5_Window_ts = EMA_5.5_Window %>% 
  select(ID, PRE_Mean, POST_Mean) %>% 
  pivot_longer(!ID, names_to = "Interval", values_to = "Mean") %>% 
  mutate(ID = as.factor(ID),
         Interval = rep(c(1,2), times = nrow(EMA_5.5_Window)))

save(EMA_5.5_Window_ts, file = "Time Series Dataframes/k20_EMA_5.5_Window_n100_ts.RData")

###

load("Time Series Dataframes/k20_EMA_5.5_Window_n100_ts.RData")

# Repeated measures with box− and violin plots
EMA_5.5_Window_ts$jit = jitter(EMA_5.5_Window_ts$Interval, amount = .09)

Pre_Post_Box_Violin = ggplot(data = EMA_5.5_Window_ts, aes(y = Mean)) +
  geom_point(data = EMA_5.5_Window_ts %>% filter(Interval == "1"), aes(x = jit), color = "dodgerblue", size = 1,
             alpha = .5) +
  geom_point(data = EMA_5.5_Window_ts %>% filter(Interval == "2"), aes(x = jit), color = "darkorange", size = 1,
             alpha = .5) +
  geom_line(aes(x = jit, group = ID), color = "lightgray", alpha = .05) +
  geom_half_boxplot(
    data = EMA_5.5_Window_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.25),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = TRUE, width = .1,
    fill = "dodgerblue", alpha = .5) +
  geom_half_boxplot(
    data = EMA_5.5_Window_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .15),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = TRUE, width = .1,
    fill = "darkorange", alpha = .5) +
  geom_half_violin(
    data = EMA_5.5_Window_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = 1.3),
    side = "r", fill = "dodgerblue", alpha = .5, trim = FALSE) +
  geom_half_violin(
    data = EMA_5.5_Window_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .3),
    side = "r", fill = "darkorange", alpha = .5, trim = FALSE) +
  scale_x_continuous(breaks = c(1,2), labels = c("PRE", "POST"), limits = c(0, 3)) +
  xlab("Interval") + ylab("PHQ-9 Mean Score") +
  #ggtitle("EMA Data (5+5 Timepoint Random Windows): Individual Pre-Post Means") +
  #theme_classic() +
  theme_bw() +
  coord_cartesian(ylim = c(0, 24))

ggsave("Time Series Dataframes/k20_EMA_5.5_Window_n100_Pre-Post_Box_Violin.jpg", plot = Pre_Post_Box_Violin, width = 6, height = 4)
save(Pre_Post_Box_Violin, file = "Time Series Dataframes/k20_EMA_5.5_Window_n100_Pre_Post_Box_Violin.RData")


# Repeated measures with box− and violin plots and means + CIs
score_mean_1 = EMA_5.5_Window_ts %>% filter(Interval == "1") %>% summarise(mean(Mean)) %>% as.numeric()
score_mean_2 = EMA_5.5_Window_ts %>% filter(Interval == "2") %>% summarise(mean(Mean)) %>% as.numeric()
score_median1 = EMA_5.5_Window_ts %>% filter(Interval == "1") %>% summarise(median(Mean)) %>% as.numeric()
score_median2 = EMA_5.5_Window_ts %>% filter(Interval == "2") %>% summarise(median(Mean)) %>% as.numeric()
score_sd_1 = EMA_5.5_Window_ts %>% filter(Interval == "1") %>% summarise(sd(Mean)) %>% as.numeric()
score_sd_2 = EMA_5.5_Window_ts %>% filter(Interval == "2") %>% summarise(sd(Mean)) %>% as.numeric()
score_se_1 = score_sd_1/sqrt(nrow(EMA_5.5_Window))
score_se_2 = score_sd_2/sqrt(nrow(EMA_5.5_Window))
score_ci_1 = EMA_5.5_Window_ts %>% filter(Interval == "1") %>% pull(Mean) %>% CI(., ci = 0.95)
score_ci_2 = EMA_5.5_Window_ts %>% filter(Interval == "2") %>% pull(Mean) %>% CI(., ci = 0.95)
#Create data frame with 2 rows and 7 columns containing the descriptives
group = c("PRE", "POST")
N = c(nrow(EMA_5.5_Window), nrow(EMA_5.5_Window))
score_mean = c(score_mean_1, score_mean_2)
score_median = c(score_median1, score_median2)
sd = c(score_sd_1, score_sd_2)
se = c(score_se_1, score_se_2)
ci = c(as.numeric(score_ci_1[1] - score_ci_1[3]), as.numeric(score_ci_2[1] - score_ci_2[3]))
summary_df = data.frame(group, N, score_mean, score_median, sd, se, ci)

# EMA_5.5_Window_ts$jit = jitter(EMA_5.5_Window_ts$Interval, amount = .09)     #already created above
x_tick_means = c(.87, 2.13)

Pre_Post_Box_Violin_Mean_CI = ggplot(data = EMA_5.5_Window_ts, aes(y = Mean)) +
  geom_point(data = EMA_5.5_Window_ts %>% filter(Interval == "1"), aes(x = jit), color = "dodgerblue", size = 1,
             alpha = .6) +
  geom_point(data = EMA_5.5_Window_ts %>% filter(Interval == "2"), aes(x = jit), color = "darkorange", size = 1,
             alpha = .6) +
  geom_line(aes(x = jit, group = ID), color = "lightgray", alpha = .05) +
  geom_half_boxplot(
    data = EMA_5.5_Window_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.28),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = FALSE, width = .2,
    fill = "dodgerblue") +
  geom_half_boxplot(
    data = EMA_5.5_Window_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .18),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = FALSE, width = .2,
    fill = "darkorange") +
  geom_half_violin(
    data = EMA_5.5_Window_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.3),
    side = "l", fill = "dodgerblue") +
  geom_half_violin(
    data = EMA_5.5_Window_ts %>% filter(Interval == "2"),aes(x = Interval, y = Mean), position = position_nudge(x = .3),
    side = "r", fill = "darkorange") +
  geom_point(data = EMA_5.5_Window_ts %>% filter(Interval == "1"), aes(x = Interval, y = score_mean[1]),
             position = position_nudge(x = -.13), color = "dodgerblue", alpha = .6, size = 1.5) +
  geom_errorbar(data = EMA_5.5_Window_ts %>% filter(Interval == "1"), aes(x = Interval, y = score_mean[1],
                                                 ymin = score_mean[1]-ci[1], ymax = score_mean[1]+ci[1]),
                position = position_nudge(-.13), color = "dodgerblue", width = 0.05, size = 0.4, alpha = .6) +
  geom_point(data = EMA_5.5_Window_ts %>% filter(Interval == "2"), aes(x = Interval, y = score_mean[2]),
             position = position_nudge(x = .13), color = "darkorange", alpha = .6, size = 1.5)+
  geom_errorbar(data = EMA_5.5_Window_ts %>% filter(Interval == "2"), aes(x = Interval, y = score_mean[2],
                                                 ymin = score_mean[2]-ci[2], ymax = score_mean[2]+ci[2]), 
                position = position_nudge(.13), color = "darkorange", width = 0.05, size = 0.4, alpha = .6) +
  geom_line(data = summary_df, aes(x = x_tick_means, y = score_mean), color = "gray", size = 1) +
  scale_x_continuous(breaks = c(1,2), labels = c("PRE", "POST"), limits = c(0, 3)) +
  xlab("Interval") + ylab("PHQ-9 Mean Score") +
  #ggtitle("EMA Data (5+5 Timepoint Random Windows): Individual Pre-Post Means") +
  #theme_classic() +
  theme_bw() +
  coord_cartesian(ylim = c(0, 24))

ggsave("Time Series Dataframes/k20_EMA_5.5_Window_n100_Pre-Post_Box_Violin_Mean+CI.jpg", plot = Pre_Post_Box_Violin_Mean_CI, width = 6, height = 4)
save(Pre_Post_Box_Violin_Mean_CI, file = "Time Series Dataframes/k20_EMA_5.5_Window_n100_Pre_Post_Box_Violin_Mean_CI.RData")

#knitr::include_graphics("Time Series Dataframes/k20_EMA_5.5_Window_n100_Pre-Post_Box_Violin.jpg")
knitr::include_graphics("Time Series Dataframes/k20_EMA_5.5_Window_n100_Pre-Post_Box_Violin_Mean+CI.jpg")

1.2.4 Zufallsauswahl: Random Days (je 5 MZP)

EMA_5.5_Days %>%
  within(., {ind.pretestSD = round(ind.pretestSD, digits = 2)
            ind.posttestSD = round(ind.posttestSD, digits = 2)}) %>% 
  head() %>% 
  kable() %>% 
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE) %>% 
  scroll_box(width = "100%")

ID	Pre_MZP1	Pre_MZP2	Pre_MZP3	Pre_MZP4	Pre_MZP5	Post_MZP1	Post_MZP2	Post_MZP3	Post_MZP4	Post_MZP5	PRE1_1	PRE1_2	PRE1_3	PRE1_4	PRE1_5	POST1_1	POST1_2	POST1_3	POST1_4	POST1_5	PRE_Mean	POST_Mean	MeanDiff	ind.pretestSD	ind.posttestSD
16	PRE1_6	PRE1_14	PRE1_15	PRE1_24	PRE1_29	POST1_5	POST1_11	POST1_16	POST1_17	POST1_22	10	11	9	13	13	13	7	9	6	9	11.2	8.8	2.4	1.79	2.68
33	PRE1_17	PRE1_22	PRE1_25	PRE1_27	PRE1_30	POST1_12	POST1_21	POST1_27	POST1_28	POST1_30	6	8	11	6	8	4	4	4	7	2	7.8	4.2	3.6	2.05	1.79
82	PRE1_17	PRE1_20	PRE1_22	PRE1_26	PRE1_30	POST1_8	POST1_15	POST1_19	POST1_25	POST1_30	12	12	13	12	10	9	5	4	7	7	11.8	6.4	5.4	1.10	1.95
103	PRE1_2	PRE1_9	PRE1_10	PRE1_16	PRE1_23	POST1_2	POST1_8	POST1_15	POST1_17	POST1_23	11	14	11	11	10	7	7	7	7	11	11.4	7.8	3.6	1.52	1.79
259	PRE1_7	PRE1_11	PRE1_12	PRE1_19	PRE1_24	POST1_1	POST1_9	POST1_17	POST1_21	POST1_29	4	7	10	6	6	15	7	11	9	15	6.6	11.4	-4.8	2.19	3.58
299	PRE1_4	PRE1_7	PRE1_19	PRE1_26	PRE1_28	POST1_12	POST1_22	POST1_25	POST1_26	POST1_27	7	9	13	14	10	18	11	2	10	3	10.6	8.8	1.8	2.88	6.53

Pre-Post-Verläufe für 9 zufällig gezogene Personen

rand = sample(EMA_5.5_Days$ID, 9)

x = tibble(ID = c(rep(rand[1],times=11),
                  rep(rand[2],times=11),
                  rep(rand[3],times=11),
                  rep(rand[4],times=11),
                  rep(rand[5],times=11),
                  rep(rand[6],times=11),
                  rep(rand[7],times=11),
                  rep(rand[8],times=11),
                  rep(rand[9],times=11)),
           MZP = rep(seq(as.Date("2020-01-01"), length.out=11, by="1 day"), times=9),
           Score = c(as.numeric(EMA_5.5_Days[rand[1],pre_5mzp]), NA, as.numeric(EMA_5.5_Days[rand[1],post_5mzp]),
                     as.numeric(EMA_5.5_Days[rand[2],pre_5mzp]), NA, as.numeric(EMA_5.5_Days[rand[2],post_5mzp]),
                     as.numeric(EMA_5.5_Days[rand[3],pre_5mzp]), NA, as.numeric(EMA_5.5_Days[rand[3],post_5mzp]),
                     as.numeric(EMA_5.5_Days[rand[4],pre_5mzp]), NA, as.numeric(EMA_5.5_Days[rand[4],post_5mzp]),
                     as.numeric(EMA_5.5_Days[rand[5],pre_5mzp]), NA, as.numeric(EMA_5.5_Days[rand[5],post_5mzp]),
                     as.numeric(EMA_5.5_Days[rand[6],pre_5mzp]), NA, as.numeric(EMA_5.5_Days[rand[6],post_5mzp]),
                     as.numeric(EMA_5.5_Days[rand[7],pre_5mzp]), NA, as.numeric(EMA_5.5_Days[rand[7],post_5mzp]),
                     as.numeric(EMA_5.5_Days[rand[8],pre_5mzp]), NA, as.numeric(EMA_5.5_Days[rand[8],post_5mzp]),
                     as.numeric(EMA_5.5_Days[rand[9],pre_5mzp]), NA, as.numeric(EMA_5.5_Days[rand[9],post_5mzp])))

x %>%
  group_by(ID) %>% 
  plot_time_series(MZP, Score,
    #.color_var = ID,           # for multiple lines in one plot
    #.color_lab = "ID",
    .facet_ncol = 3,
    .facet_scales = "fixed",
    .interactive = TRUE,
    .facet_collapse = FALSE,
    .smooth = TRUE,
    .smooth_degree = 2,
    .smooth_alpha = 0.5,
    .smooth_size = 0.2
  )

# don´t run this section (code for extremely computation-intense plots that I already stored as .RData and .jpg)
# repeated-measures scatter-boxplot-violin-histograms for individual PRE and POST means
# from van Langen (2020) Open-visualizations tutorial for repeated measures in R

# EMA_5.5_Days
# converting my dataframes to use in the same ggplot structure:
EMA_5.5_Days_ts = EMA_5.5_Days %>% 
  select(ID, PRE_Mean, POST_Mean) %>% 
  pivot_longer(!ID, names_to = "Interval", values_to = "Mean") %>% 
  mutate(ID = as.factor(ID),
         Interval = rep(c(1,2), times = nrow(EMA_5.5_Days)))

save(EMA_5.5_Days_ts, file = "Time Series Dataframes/k20_EMA_5.5_Days_n100_ts.RData")

###

load("Time Series Dataframes/k20_EMA_5.5_Days_n100_ts.RData")

# Repeated measures with box− and violin plots
EMA_5.5_Days_ts$jit = jitter(EMA_5.5_Days_ts$Interval, amount = .09)

Pre_Post_Box_Violin = ggplot(data = EMA_5.5_Days_ts, aes(y = Mean)) +
  geom_point(data = EMA_5.5_Days_ts %>% filter(Interval == "1"), aes(x = jit), color = "dodgerblue", size = 1,
             alpha = .5) +
  geom_point(data = EMA_5.5_Days_ts %>% filter(Interval == "2"), aes(x = jit), color = "darkorange", size = 1,
             alpha = .5) +
  geom_line(aes(x = jit, group = ID), color = "lightgray", alpha = .05) +
  geom_half_boxplot(
    data = EMA_5.5_Days_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.25),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = TRUE, width = .1,
    fill = "dodgerblue", alpha = .5) +
  geom_half_boxplot(
    data = EMA_5.5_Days_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .15),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = TRUE, width = .1,
    fill = "darkorange", alpha = .5) +
  geom_half_violin(
    data = EMA_5.5_Days_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = 1.3),
    side = "r", fill = "dodgerblue", alpha = .5, trim = FALSE) +
  geom_half_violin(
    data = EMA_5.5_Days_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .3),
    side = "r", fill = "darkorange", alpha = .5, trim = FALSE) +
  scale_x_continuous(breaks = c(1,2), labels = c("PRE", "POST"), limits = c(0, 3)) +
  xlab("Interval") + ylab("PHQ-9 Mean Score") +
  #ggtitle("EMA Data (5+5 Timepoint Random Days): Individual Pre-Post Means") +
  #theme_classic() +
  theme_bw() +
  coord_cartesian(ylim = c(0, 24))

ggsave("Time Series Dataframes/k20_EMA_5.5_Days_n100_Pre-Post_Box_Violin.jpg", plot = Pre_Post_Box_Violin, width = 6, height = 4)
save(Pre_Post_Box_Violin, file = "Time Series Dataframes/k20_EMA_5.5_Days_n100_Pre_Post_Box_Violin.RData")


# Repeated measures with box− and violin plots and means + CIs
score_mean_1 = EMA_5.5_Days_ts %>% filter(Interval == "1") %>% summarise(mean(Mean)) %>% as.numeric()
score_mean_2 = EMA_5.5_Days_ts %>% filter(Interval == "2") %>% summarise(mean(Mean)) %>% as.numeric()
score_median1 = EMA_5.5_Days_ts %>% filter(Interval == "1") %>% summarise(median(Mean)) %>% as.numeric()
score_median2 = EMA_5.5_Days_ts %>% filter(Interval == "2") %>% summarise(median(Mean)) %>% as.numeric()
score_sd_1 = EMA_5.5_Days_ts %>% filter(Interval == "1") %>% summarise(sd(Mean)) %>% as.numeric()
score_sd_2 = EMA_5.5_Days_ts %>% filter(Interval == "2") %>% summarise(sd(Mean)) %>% as.numeric()
score_se_1 = score_sd_1/sqrt(nrow(EMA_5.5_Days))
score_se_2 = score_sd_2/sqrt(nrow(EMA_5.5_Days))
score_ci_1 = EMA_5.5_Days_ts %>% filter(Interval == "1") %>% pull(Mean) %>% CI(., ci = 0.95)
score_ci_2 = EMA_5.5_Days_ts %>% filter(Interval == "2") %>% pull(Mean) %>% CI(., ci = 0.95)
#Create data frame with 2 rows and 7 columns containing the descriptives
group = c("PRE", "POST")
N = c(nrow(EMA_5.5_Days), nrow(EMA_5.5_Days))
score_mean = c(score_mean_1, score_mean_2)
score_median = c(score_median1, score_median2)
sd = c(score_sd_1, score_sd_2)
se = c(score_se_1, score_se_2)
ci = c(as.numeric(score_ci_1[1] - score_ci_1[3]), as.numeric(score_ci_2[1] - score_ci_2[3]))
summary_df = data.frame(group, N, score_mean, score_median, sd, se, ci)

# EMA_5.5_Days_ts$jit = jitter(EMA_5.5_Days_ts$Interval, amount = .09)     #already created above
x_tick_means = c(.87, 2.13)

Pre_Post_Box_Violin_Mean_CI = ggplot(data = EMA_5.5_Days_ts, aes(y = Mean)) +
  geom_point(data = EMA_5.5_Days_ts %>% filter(Interval == "1"), aes(x = jit), color = "dodgerblue", size = 1,
             alpha = .6) +
  geom_point(data = EMA_5.5_Days_ts %>% filter(Interval == "2"), aes(x = jit), color = "darkorange", size = 1,
             alpha = .6) +
  geom_line(aes(x = jit, group = ID), color = "lightgray", alpha = .05) +
  geom_half_boxplot(
    data = EMA_5.5_Days_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.28),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = FALSE, width = .2,
    fill = "dodgerblue") +
  geom_half_boxplot(
    data = EMA_5.5_Days_ts %>% filter(Interval == "2"), aes(x = Interval, y = Mean), position = position_nudge(x = .18),
    side = "r", outlier.shape = NA, center = TRUE, errorbar.draw = FALSE, width = .2,
    fill = "darkorange") +
  geom_half_violin(
    data = EMA_5.5_Days_ts %>% filter(Interval == "1"), aes(x = Interval, y = Mean), position = position_nudge(x = -.3),
    side = "l", fill = "dodgerblue") +
  geom_half_violin(
    data = EMA_5.5_Days_ts %>% filter(Interval == "2"),aes(x = Interval, y = Mean), position = position_nudge(x = .3),
    side = "r", fill = "darkorange") +
  geom_point(data = EMA_5.5_Days_ts %>% filter(Interval == "1"), aes(x = Interval, y = score_mean[1]),
             position = position_nudge(x = -.13), color = "dodgerblue", alpha = .6, size = 1.5) +
  geom_errorbar(data = EMA_5.5_Days_ts %>% filter(Interval == "1"), aes(x = Interval, y = score_mean[1],
                                                 ymin = score_mean[1]-ci[1], ymax = score_mean[1]+ci[1]),
                position = position_nudge(-.13), color = "dodgerblue", width = 0.05, size = 0.4, alpha = .6) +
  geom_point(data = EMA_5.5_Days_ts %>% filter(Interval == "2"), aes(x = Interval, y = score_mean[2]),
             position = position_nudge(x = .13), color = "darkorange", alpha = .6, size = 1.5)+
  geom_errorbar(data = EMA_5.5_Days_ts %>% filter(Interval == "2"), aes(x = Interval, y = score_mean[2],
                                                 ymin = score_mean[2]-ci[2], ymax = score_mean[2]+ci[2]), 
                position = position_nudge(.13), color = "darkorange", width = 0.05, size = 0.4, alpha = .6) +
  geom_line(data = summary_df, aes(x = x_tick_means, y = score_mean), color = "gray", size = 1) +
  scale_x_continuous(breaks = c(1,2), labels = c("PRE", "POST"), limits = c(0, 3)) +
  xlab("Interval") + ylab("PHQ-9 Mean Score") +
  #ggtitle("EMA Data (5+5 Timepoint Random Days): Individual Pre-Post Means") +
  #theme_classic() +
  theme_bw() +
  coord_cartesian(ylim = c(0, 24))

ggsave("Time Series Dataframes/k20_EMA_5.5_Days_n100_Pre-Post_Box_Violin_Mean+CI.jpg", plot = Pre_Post_Box_Violin_Mean_CI, width = 6, height = 4)
save(Pre_Post_Box_Violin_Mean_CI, file = "Time Series Dataframes/k20_EMA_5.5_n100_Days_Pre_Post_Box_Violin_Mean_CI.RData")

#knitr::include_graphics("Time Series Dataframes/k20_EMA_5.5_Days_n100_Pre-Post_Box_Violin.jpg")
knitr::include_graphics("Time Series Dataframes/k20_EMA_5.5_Days_n100_Pre-Post_Box_Violin_Mean+CI.jpg")

1.3 Deskriptive Statistiken der Datensets

tibble(Descriptives = c("mean_PRE_Mean","mean_POST_Mean","mean_MeanDiff","mean_ind.pretestSD","mean_ind.posttestSD"),
       EMA_5.5 = round(c(mean(EMA_5.5$PRE_Mean),mean(EMA_5.5$POST_Mean),mean(EMA_5.5$MeanDiff),
                        mean(EMA_5.5$ind.pretestSD),mean(EMA_5.5$ind.posttestSD)), digits = 3),
       EMA_30.30 = round(c(mean(EMA_30.30$PRE_Mean),mean(EMA_30.30$POST_Mean),mean(EMA_30.30$MeanDiff),
                          mean(EMA_30.30$ind.pretestSD),mean(EMA_30.30$ind.posttestSD)), digits = 3),
       EMA_5.5_Window = round(c(mean(EMA_5.5_Window$PRE_Mean),mean(EMA_5.5_Window$POST_Mean),
                             mean(EMA_5.5_Window$MeanDiff),mean(EMA_5.5_Window$ind.pretestSD),
                             mean(EMA_5.5_Window$ind.posttestSD)), digits = 3),
       EMA_5.5_Days = round(c(mean(EMA_5.5_Days$PRE_Mean),mean(EMA_5.5_Days$POST_Mean),mean(EMA_5.5_Days$MeanDiff),
                           mean(EMA_5.5_Days$ind.pretestSD),mean(EMA_5.5_Days$ind.posttestSD)), digits = 3)) %>%
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

Descriptives	EMA_5.5	EMA_30.30	EMA_5.5_Window	EMA_5.5_Days
mean_PRE_Mean	10.558	10.558	10.534	10.426
mean_POST_Mean	7.444	7.444	7.542	7.208
mean_MeanDiff	3.114	3.114	2.992	3.218
mean_ind.pretestSD	2.625	2.388	2.443	2.239
mean_ind.posttestSD	3.588	3.264	3.327	3.195

Boxplots der Pre- und Post-Mittelwerte

# Boxplots zum Vergleich
temp = tibble(Scores = c(EMA_5.5$PRE_Mean, EMA_30.30$PRE_Mean, EMA_5.5_Window$PRE_Mean, EMA_5.5_Days$PRE_Mean),
              Datasets = rep(c("EMA_5.5", "EMA_30.30", "EMA_5.5_Window", "EMA_5.5_Days"), each =
                               length(EMA_5.5$PRE_Mean)))

ggplot(temp, aes(x = Datasets, y = Scores)) + 
  geom_boxplot() + 
  ylim(0, 27) +
  ggtitle("PHQ-9 PRE-Mean") +
  xlab("Dataset") +
  ylab("PHQ-9 Scores")

temp = tibble(Scores = c(EMA_5.5$POST_Mean, EMA_30.30$POST_Mean, EMA_5.5_Window$POST_Mean,
                         EMA_5.5_Days$POST_Mean), Datasets = rep(c("EMA_5.5", "EMA_30.30", "EMA_5.5_Window",
                         "EMA_5.5_Days"), each = length(EMA_5.5$POST_Mean)))

ggplot(temp, aes(x = Datasets, y = Scores)) + 
  geom_boxplot() + 
  ylim(0, 27) +
  ggtitle("PHQ-9 POST-Mean") +
  xlab("Dataset") +
  ylab("PHQ-9 Scores")

Prozentuale Überlappung der Pre-Mittelwerte

# Overlap-Plots zum Vergleich
final.plot(list(EMA_5.5_PRE_Mean = EMA_5.5$PRE_Mean, EMA_30.30_PRE_Mean = EMA_30.30$PRE_Mean), 
           overlap(list(EMA_5.5_PRE_Mean = EMA_5.5$PRE_Mean, EMA_30.30_PRE_Mean = EMA_30.30$PRE_Mean))$OV)

final.plot(list(EMA_5.5_PRE_Mean = EMA_5.5$PRE_Mean, EMA_5.5_Window_PRE_Mean = EMA_5.5_Window$PRE_Mean), 
           overlap(list(EMA_5.5_PRE_Mean = EMA_5.5$PRE_Mean, EMA_5.5_Window_PRE_Mean =
                          EMA_5.5_Window$PRE_Mean))$OV)

final.plot(list(EMA_5.5_PRE_Mean = EMA_5.5$PRE_Mean, EMA_5.5_Days_PRE_Mean = EMA_5.5_Days$PRE_Mean), 
           overlap(list(EMA_5.5_PRE_Mean = EMA_5.5$PRE_Mean, EMA_5.5_Days_PRE_Mean =
                          EMA_5.5_Days$PRE_Mean))$OV)

Prozentuale Überlappung der Post-Mittelwerte

# Overlap-Plots zum Vergleich
final.plot(list(EMA_5.5_POST_Mean = EMA_5.5$POST_Mean, EMA_30MZP_POST_Mean = EMA_30.30$POST_Mean), 
           overlap(list(EMA_5.5_POST_Mean = EMA_5.5$POST_Mean, EMA_30MZP_POST_Mean =
                          EMA_30.30$POST_Mean))$OV)

final.plot(list(EMA_5.5_POST_Mean = EMA_5.5$POST_Mean, EMA_Window_POST_Mean = EMA_5.5_Window$POST_Mean), 
           overlap(list(EMA_5.5_POST_Mean = EMA_5.5$POST_Mean, EMA_Window_POST_Mean =
                          EMA_5.5_Window$POST_Mean))$OV)

final.plot(list(EMA_5.5_POST_Mean = EMA_5.5$POST_Mean, EMA_Days_POST_Mean = EMA_5.5_Days$POST_Mean), 
           overlap(list(EMA_5.5_POST_Mean = EMA_5.5$POST_Mean, EMA_Days_POST_Mean = EMA_5.5_Days$POST_Mean))$OV)

1.4 Reliabilitäten und Inter-Item-Korrelationen

1.4.1 EMA_5.5 (je 5 MZP)

# Korrelationsmatrix von PRE- und POST-MZP:
EMA_5.5_KorMat = cor(EMA_5.5[, c(pre_5mzp, post_5mzp)]) %>% 
  round(., digits = 2)

# durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden MZP (beachte: ohne Fisher-Z-Transformation):
pre_inter_item_rtt = 0L
for (i in 1:4) {
  pre_inter_item_rtt = pre_inter_item_rtt + FisherZ(EMA_5.5_KorMat[i,i+1])
}
pre_inter_item_rtt = FisherZInv(pre_inter_item_rtt / 4)

post_inter_item_rtt = 0L
for (i in 5:9) {
  post_inter_item_rtt = post_inter_item_rtt + FisherZ(EMA_5.5_KorMat[i,i+1])
}
post_inter_item_rtt = FisherZInv(post_inter_item_rtt / 4)


for (i in 1:9) {
  EMA_5.5_KorMat[i, i+1] = cell_spec(EMA_5.5_KorMat[i, i+1], "html", bold = TRUE)
}

rownames(EMA_5.5_KorMat) = cell_spec(rownames(EMA_5.5_KorMat), "html", bold = TRUE)

EMA_5.5_KorMat %>%
  kable(., format = "html", escape = FALSE) %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
                full_width = FALSE, fixed_thead = T)

	PRE1_1	PRE1_2	PRE1_3	PRE1_4	PRE1_5	POST1_1	POST1_2	POST1_3	POST1_4	POST1_5
PRE1_1	1	0.46	0.23	-0.03	-0.04	0.13	-0.02	-0.13	-0.1	0.04
PRE1_2	0.46	1	0.49	0.26	0.24	-0.07	-0.01	-0.02	-0.13	-0.01
PRE1_3	0.23	0.49	1	0.28	0.05	-0.2	-0.08	-0.09	-0.02	0.06
PRE1_4	-0.03	0.26	0.28	1	0.28	-0.08	-0.04	0.06	0.14	0.17
PRE1_5	-0.04	0.24	0.05	0.28	1	-0.11	-0.13	0.06	0.12	0.12
POST1_1	0.13	-0.07	-0.2	-0.08	-0.11	1	0.5	0.21	-0.1	-0.05
POST1_2	-0.02	-0.01	-0.08	-0.04	-0.13	0.5	1	0.37	0.09	-0.11
POST1_3	-0.13	-0.02	-0.09	0.06	0.06	0.21	0.37	1	0.34	-0.05
POST1_4	-0.1	-0.13	-0.02	0.14	0.12	-0.1	0.09	0.34	1	0.26
POST1_5	0.04	-0.01	0.06	0.17	0.12	-0.05	-0.11	-0.05	0.26	1

# mittleres Cronbach´s Alpha zwischen Pre-MZP und Post-MZP:
PRE_alpha = CronbachAlpha(EMA_5.5[pre_5mzp])
POST_alpha = CronbachAlpha(EMA_5.5[post_5mzp])
EMA_5.5_Alpha = FisherZInv(mean(c(FisherZ(PRE_alpha), FisherZ(POST_alpha))))

Korrelation zwischen den Pre- und Post-Intervall-Mittelwerten = -0.046.
Durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden Pre-MZP (Fisher-Z-transformiert): r = 0.38.
Durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden Post-MZP (Fisher-Z-transformiert): r = 0.35.
Mittleres Cronbach´s Alpha zwischen Pre-MZP und Post-MZP = 0.539.

1.4.2 EMA_30.30 (je 30 MZP)

# Korrelationsmatrix von PRE- und POST-MZP:
EMA_30.30_KorMat = cor(EMA_30.30[, c(pre_30mzp, post_30mzp)]) %>% 
  round(., digits = 2)


# durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden MZP (beachte: ohne Fisher-Z-Transformation):
pre_inter_item_rtt = 0L
for (i in 1:29) {
  pre_inter_item_rtt = pre_inter_item_rtt + FisherZ(EMA_30.30_KorMat[i,i+1])
}
pre_inter_item_rtt = FisherZInv(pre_inter_item_rtt / 29)

post_inter_item_rtt = 0L
for (i in 31:59) {
  post_inter_item_rtt = post_inter_item_rtt + FisherZ(EMA_30.30_KorMat[i,i+1])
}
post_inter_item_rtt = FisherZInv(post_inter_item_rtt / 29)


for (i in 1:59) {
  EMA_30.30_KorMat[i, i+1] = cell_spec(EMA_30.30_KorMat[i, i+1], "html", bold = TRUE)
}

rownames(EMA_30.30_KorMat) = cell_spec(rownames(EMA_30.30_KorMat), "html", bold = TRUE)

EMA_30.30_KorMat %>%
  kable(., format = "html", escape = FALSE) %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
                full_width = FALSE, fixed_thead = T) %>%
  scroll_box(height = "800px")

	PRE1_1	PRE1_2	PRE1_3	PRE1_4	PRE1_5	PRE1_6	PRE1_7	PRE1_8	PRE1_9	PRE1_10	PRE1_11	PRE1_12	PRE1_13	PRE1_14	PRE1_15	PRE1_16	PRE1_17	PRE1_18	PRE1_19	PRE1_20	PRE1_21	PRE1_22	PRE1_23	PRE1_24	PRE1_25	PRE1_26	PRE1_27	PRE1_28	PRE1_29	PRE1_30	POST1_1	POST1_2	POST1_3	POST1_4	POST1_5	POST1_6	POST1_7	POST1_8	POST1_9	POST1_10	POST1_11	POST1_12	POST1_13	POST1_14	POST1_15	POST1_16	POST1_17	POST1_18	POST1_19	POST1_20	POST1_21	POST1_22	POST1_23	POST1_24	POST1_25	POST1_26	POST1_27	POST1_28	POST1_29	POST1_30
PRE1_1	1	0.46	0.23	-0.03	-0.04	0.3	0.36	0.38	0.34	0.25	0.39	0.38	0.42	0.21	0.23	0.38	0.34	0.31	0.35	0.25	0.27	0.19	0.35	0.42	0.37	0.2	0.4	0.37	0.35	0.32	0.13	-0.02	-0.13	-0.1	0.04	0.02	0.09	-0.12	-0.01	-0.04	-0.07	0.1	-0.1	-0.01	0.01	-0.14	-0.09	-0.02	0.02	0.17	0.03	-0.06	-0.01	-0.03	0	-0.1	0.01	-0.04	-0.01	0.05
PRE1_2	0.46	1	0.49	0.26	0.24	0.51	0.55	0.63	0.49	0.34	0.61	0.54	0.52	0.48	0.37	0.58	0.48	0.48	0.68	0.31	0.41	0.47	0.64	0.56	0.41	0.38	0.52	0.63	0.58	0.44	-0.07	-0.01	-0.02	-0.13	-0.01	-0.11	-0.06	0.07	-0.13	0	-0.05	-0.02	-0.16	-0.03	0.04	-0.14	-0.09	-0.1	0.02	0.07	0.03	-0.06	-0.26	0	0.07	-0.02	0.05	-0.12	-0.11	-0.04
PRE1_3	0.23	0.49	1	0.28	0.05	0.46	0.62	0.46	0.32	0.26	0.54	0.46	0.39	0.47	0.26	0.38	0.41	0.6	0.38	0.34	0.46	0.42	0.42	0.46	0.36	0.42	0.43	0.39	0.44	0.44	-0.2	-0.08	-0.09	-0.02	0.06	-0.08	-0.02	-0.01	-0.21	-0.01	-0.06	0	-0.17	-0.08	-0.04	-0.08	-0.08	0.01	-0.16	-0.02	-0.03	-0.19	-0.25	0.05	0.08	0.01	-0.09	-0.24	0.03	-0.05
PRE1_4	-0.03	0.26	0.28	1	0.28	0.25	0.42	0.35	0.38	0.44	0.19	0.34	0.47	0.42	0.39	0.13	0.43	0.43	0.46	0.37	0.4	0.49	0.39	0.27	0.27	0.44	0.26	0.42	0.41	0.28	-0.08	-0.04	0.06	0.14	0.17	0.05	0.08	0.02	0.04	0.05	0.04	0.07	0.1	-0.04	0.07	0.03	0.1	0.14	-0.02	-0.01	0.18	0.03	0.02	-0.07	0.06	0.02	0.02	-0.04	0.02	0.21
PRE1_5	-0.04	0.24	0.05	0.28	1	0.34	0.28	0.35	0.25	0.25	0.16	0.24	0.3	0.41	0.35	0.24	0.38	0.33	0.36	0.15	0.3	0.35	0.34	0.23	0.26	0.3	0.27	0.33	0.27	0.3	-0.11	-0.13	0.06	0.12	0.12	0.04	-0.07	-0.08	0.03	0.09	-0.1	-0.1	-0.06	0.18	0.09	-0.12	0.01	-0.08	0.03	0.17	0.03	0.01	0.03	-0.08	0.02	0.04	-0.06	0.06	-0.09	0.07
PRE1_6	0.3	0.51	0.46	0.25	0.34	1	0.52	0.37	0.05	-0.09	0.33	0.42	0.5	0.39	0.22	0.38	0.34	0.43	0.44	0.29	0.38	0.35	0.31	0.49	0.34	0.3	0.4	0.3	0.44	0.45	-0.14	-0.06	-0.03	-0.06	0.02	-0.17	-0.12	-0.03	-0.03	0.08	-0.1	-0.07	-0.13	-0.02	0.03	-0.18	-0.06	-0.04	-0.1	0.12	0.06	-0.04	-0.26	-0.08	0.03	-0.08	-0.1	-0.11	0.05	-0.03
PRE1_7	0.36	0.55	0.62	0.42	0.28	0.52	1	0.45	0.12	0.18	0.44	0.43	0.47	0.53	0.4	0.47	0.47	0.58	0.49	0.26	0.43	0.44	0.44	0.48	0.49	0.44	0.45	0.54	0.46	0.4	-0.13	-0.09	-0.04	0.03	0.1	-0.02	0	-0.11	-0.07	0.05	-0.13	-0.03	-0.1	-0.01	0.1	-0.16	-0.09	-0.04	-0.01	0.15	0.12	-0.08	-0.07	-0.08	-0.05	-0.03	-0.11	-0.1	0.06	0.02
PRE1_8	0.38	0.63	0.46	0.35	0.35	0.37	0.45	1	0.24	0.07	0.44	0.59	0.5	0.4	0.26	0.43	0.42	0.47	0.47	0.41	0.34	0.43	0.53	0.45	0.43	0.42	0.46	0.54	0.49	0.3	-0.06	-0.08	-0.07	-0.03	0.08	0	0	-0.04	-0.15	0.02	-0.05	-0.07	-0.09	0.01	0.03	-0.1	-0.06	0.04	-0.08	0.04	-0.07	-0.09	-0.11	-0.11	0.2	-0.04	-0.03	-0.13	0.02	0.01
PRE1_9	0.34	0.49	0.32	0.38	0.25	0.05	0.12	0.24	1	0.47	0.39	0.37	0.3	0.38	0.36	0.26	0.46	0.26	0.43	0.38	0.33	0.52	0.41	0.3	0.23	0.19	0.35	0.49	0.45	0.35	-0.04	-0.03	0.02	0.07	0.06	0.09	0.04	-0.02	-0.06	0.01	0.02	0.14	-0.08	-0.02	0.02	-0.08	0.02	0.03	0.05	0.06	0.03	-0.08	-0.05	0.1	0.07	0.04	0.11	-0.02	-0.23	0.15
PRE1_10	0.25	0.34	0.26	0.44	0.25	-0.09	0.18	0.07	0.47	1	0.34	0.18	0.34	0.31	0.4	0.18	0.39	0.45	0.42	0.11	0.4	0.23	0.49	0.25	0.17	0.4	0.26	0.3	0.25	0.32	0.03	0	0.02	0.01	0.12	0.03	0.12	0.1	0.01	-0.09	0.03	0.1	0	0.04	-0.01	0.08	0.06	-0.03	0.04	0	0.11	0.01	0	0.07	-0.03	0.09	0.09	-0.04	-0.08	0.1
PRE1_11	0.39	0.61	0.54	0.19	0.16	0.33	0.44	0.44	0.39	0.34	1	0.49	0.31	0.17	0.03	0.4	0.32	0.36	0.51	0.34	0.45	0.33	0.4	0.45	0.29	0.15	0.33	0.46	0.62	0.42	0	-0.04	-0.04	0.03	0.18	-0.11	0.1	0.09	-0.03	0.08	0.15	0.1	-0.06	-0.08	0.03	-0.03	0.03	0.05	0.07	0	0	-0.04	-0.07	0.08	0.15	-0.01	0.11	-0.11	0	0.12
PRE1_12	0.38	0.54	0.46	0.34	0.24	0.42	0.43	0.59	0.37	0.18	0.49	1	0.41	0.07	0.05	0.45	0.44	0.34	0.42	0.36	0.26	0.43	0.55	0.4	0.34	0.23	0.52	0.52	0.39	0.39	-0.05	-0.09	-0.13	-0.04	0.11	-0.12	0.07	-0.13	-0.13	0.1	-0.09	0.02	-0.14	-0.05	0.04	-0.14	-0.05	0	-0.05	0.04	0.04	-0.13	-0.2	-0.03	0.11	-0.13	-0.04	-0.07	-0.08	0.1
PRE1_13	0.42	0.52	0.39	0.47	0.3	0.5	0.47	0.5	0.3	0.34	0.31	0.41	1	0.29	0.08	0.19	0.46	0.55	0.51	0.39	0.26	0.32	0.62	0.52	0.37	0.38	0.37	0.49	0.52	0.38	-0.07	-0.07	-0.15	-0.13	-0.01	-0.19	-0.12	-0.03	-0.07	-0.03	0	-0.1	-0.14	-0.06	-0.14	-0.12	-0.1	-0.12	-0.13	0.03	0.03	-0.12	-0.21	-0.09	-0.06	-0.11	-0.11	-0.16	-0.02	-0.04
PRE1_14	0.21	0.48	0.47	0.42	0.41	0.39	0.53	0.4	0.38	0.31	0.17	0.07	0.29	1	0.43	0.37	0.44	0.53	0.4	0.25	0.46	0.47	0.31	0.43	0.34	0.54	0.31	0.38	0.42	0.34	-0.14	-0.03	0.06	0.09	0.1	0.18	-0.05	0.01	-0.06	-0.02	-0.15	0.06	-0.02	0.06	0.11	-0.05	0.08	0	-0.08	0.12	0.12	0.01	-0.06	-0.11	0.09	0.09	-0.04	0	-0.01	0.03
PRE1_15	0.23	0.37	0.26	0.39	0.35	0.22	0.4	0.26	0.36	0.4	0.03	0.05	0.08	0.43	1	0.32	0.38	0.38	0.41	0.1	0.45	0.39	0.29	0.17	0.31	0.43	0.38	0.33	0.16	0.28	-0.07	-0.04	0.13	0.07	0.01	0.13	0.05	-0.04	-0.01	-0.04	-0.12	-0.02	-0.05	0.14	0.13	-0.1	-0.1	0.04	0.09	0.18	0.04	0	0.04	0.04	-0.03	0.12	0.04	-0.06	-0.05	0.04
PRE1_16	0.38	0.58	0.38	0.13	0.24	0.38	0.47	0.43	0.26	0.18	0.4	0.45	0.19	0.37	0.32	1	0.43	0.3	0.21	-0.18	0.34	0.36	0.45	0.32	0.24	0.25	0.49	0.41	0.28	0.33	-0.07	0	0.03	0.06	0.05	0.1	0.07	-0.07	-0.07	0.03	-0.2	0.02	-0.04	0.01	0.26	-0.11	-0.07	-0.03	0.05	0.24	0.08	-0.04	-0.11	0.05	0.08	0.13	-0.05	-0.06	0.04	0
PRE1_17	0.34	0.48	0.41	0.43	0.38	0.34	0.47	0.42	0.46	0.39	0.32	0.44	0.46	0.44	0.38	0.43	1	0.39	0.26	-0.02	0.31	0.53	0.56	0.3	0.34	0.56	0.53	0.46	0.28	0.22	-0.14	-0.11	-0.25	-0.13	0.07	-0.12	-0.13	-0.12	-0.07	-0.13	-0.19	-0.09	-0.31	-0.12	0.14	-0.16	-0.18	-0.26	-0.07	0.09	0.01	-0.22	-0.11	-0.14	-0.12	-0.17	-0.17	-0.15	-0.12	0.03
PRE1_18	0.31	0.48	0.6	0.43	0.33	0.43	0.58	0.47	0.26	0.45	0.36	0.34	0.55	0.53	0.38	0.3	0.39	1	0.31	0.16	0.43	0.31	0.46	0.51	0.47	0.49	0.37	0.39	0.45	0.47	-0.12	-0.04	0.06	-0.01	0.07	0.02	-0.02	0.02	-0.03	-0.05	-0.02	0.13	0.01	-0.07	-0.11	-0.09	0.05	0.03	-0.06	0.03	0.06	-0.02	-0.16	0	0.06	0.11	-0.06	-0.12	0.02	-0.01
PRE1_19	0.35	0.68	0.38	0.46	0.36	0.44	0.49	0.47	0.43	0.42	0.51	0.42	0.51	0.4	0.41	0.21	0.26	0.31	1	0.46	0.45	0.44	0.46	0.5	0.4	0.34	0.39	0.5	0.54	0.49	0.06	0.01	0.04	-0.01	0.07	-0.07	0.06	0.07	0	0.13	0.06	-0.08	-0.03	0.19	0.03	-0.05	0	0.09	0.05	0.09	0.05	0.06	-0.08	0.02	0.11	-0.05	0.14	0.02	-0.06	0.11
PRE1_20	0.25	0.31	0.34	0.37	0.15	0.29	0.26	0.41	0.38	0.11	0.34	0.36	0.39	0.25	0.1	-0.18	-0.02	0.16	0.46	1	0.34	0.3	0.24	0.35	0.21	0.12	0.13	0.41	0.53	0.27	-0.07	-0.13	0	0.11	0.13	-0.02	0.07	0	-0.13	0.11	0.11	0.07	-0.02	0.01	-0.14	-0.03	0.06	0.13	-0.07	-0.05	0.05	-0.07	-0.05	-0.04	0.11	-0.04	0.09	-0.1	-0.04	0.11
PRE1_21	0.27	0.41	0.46	0.4	0.3	0.38	0.43	0.34	0.33	0.4	0.45	0.26	0.26	0.46	0.45	0.34	0.31	0.43	0.45	0.34	1	0.36	0.2	0.24	0.12	0.41	0.37	0.24	0.43	0.41	-0.1	0.01	0.04	-0.02	0.07	0.09	0.02	0.01	-0.08	-0.03	-0.13	0.15	-0.03	0.04	-0.03	-0.2	0.03	0.04	0.08	0.07	0.04	0.01	-0.04	0	-0.01	0.07	-0.07	-0.06	-0.02	0.09
PRE1_22	0.19	0.47	0.42	0.49	0.35	0.35	0.44	0.43	0.52	0.23	0.33	0.43	0.32	0.47	0.39	0.36	0.53	0.31	0.44	0.3	0.36	1	0.4	0.08	0.11	0.39	0.43	0.46	0.38	0.29	-0.04	-0.05	0	0	0.09	0.09	-0.07	0.07	-0.07	-0.04	-0.03	0.02	-0.17	0.02	0.16	-0.01	-0.04	-0.03	-0.03	0.11	0.15	-0.06	-0.02	-0.09	0	-0.06	0.04	0.04	-0.14	0.11
PRE1_23	0.35	0.64	0.42	0.39	0.34	0.31	0.44	0.53	0.41	0.49	0.4	0.55	0.62	0.31	0.29	0.45	0.56	0.46	0.46	0.24	0.2	0.4	1	0.33	0.16	0.4	0.44	0.53	0.36	0.44	-0.1	0.01	-0.01	0.02	-0.03	-0.03	0.11	0.06	-0.2	-0.04	-0.06	-0.06	-0.16	0.06	0.11	-0.07	-0.06	-0.14	-0.02	0.17	0.05	-0.07	-0.17	-0.01	0.07	-0.02	0.02	-0.13	-0.01	0.02
PRE1_24	0.42	0.56	0.46	0.27	0.23	0.49	0.48	0.45	0.3	0.25	0.45	0.4	0.52	0.43	0.17	0.32	0.3	0.51	0.5	0.35	0.24	0.08	0.33	1	0.3	0.27	0.28	0.51	0.51	0.43	-0.05	-0.04	-0.06	0.05	0.14	-0.08	-0.05	-0.1	0.08	0.17	0.02	-0.03	0.02	0.02	-0.01	-0.11	0.01	0.11	-0.06	0.09	-0.02	-0.02	-0.11	0.04	0.14	-0.03	-0.04	-0.07	0.09	0.07
PRE1_25	0.37	0.41	0.36	0.27	0.26	0.34	0.49	0.43	0.23	0.17	0.29	0.34	0.37	0.34	0.31	0.24	0.34	0.47	0.4	0.21	0.12	0.11	0.16	0.3	1	0.28	0.39	0.39	0.42	0.21	-0.05	-0.21	-0.08	-0.05	0.11	-0.16	0.01	-0.14	-0.03	0.02	-0.03	-0.01	-0.06	-0.13	-0.07	-0.07	-0.08	0	-0.07	-0.08	0.03	-0.15	-0.14	-0.06	0.03	0.01	-0.01	-0.17	-0.08	-0.06
PRE1_26	0.2	0.38	0.42	0.44	0.3	0.3	0.44	0.42	0.19	0.4	0.15	0.23	0.38	0.54	0.43	0.25	0.56	0.49	0.34	0.12	0.41	0.39	0.4	0.27	0.28	1	0.32	0.14	0.12	0.08	-0.04	0	-0.01	-0.05	-0.05	-0.04	-0.01	0.04	-0.07	-0.07	-0.12	-0.01	-0.09	0.02	0.06	-0.1	-0.07	-0.07	-0.05	0.15	0.11	-0.07	-0.07	-0.11	0	-0.05	0.01	-0.06	0.02	-0.05
PRE1_27	0.4	0.52	0.43	0.26	0.27	0.4	0.45	0.46	0.35	0.26	0.33	0.52	0.37	0.31	0.38	0.49	0.53	0.37	0.39	0.13	0.37	0.43	0.44	0.28	0.39	0.32	1	0.38	0.22	0.07	-0.01	-0.02	-0.18	-0.1	0.02	0.02	0	-0.1	-0.11	-0.1	-0.22	-0.05	-0.1	-0.04	0.11	-0.17	-0.06	-0.15	0.03	0.05	0.03	-0.01	-0.15	-0.14	-0.04	-0.03	-0.02	-0.17	-0.03	-0.04
PRE1_28	0.37	0.63	0.39	0.42	0.33	0.3	0.54	0.54	0.49	0.3	0.46	0.52	0.49	0.38	0.33	0.41	0.46	0.39	0.5	0.41	0.24	0.46	0.53	0.51	0.39	0.14	0.38	1	0.44	0.26	-0.15	-0.11	-0.11	0.01	0.17	-0.04	-0.01	-0.07	-0.14	0.05	-0.02	0.04	-0.1	-0.11	-0.02	-0.1	-0.13	-0.02	0.01	0.04	-0.02	-0.19	-0.09	0.02	0.08	-0.05	-0.04	-0.1	-0.09	0.06
PRE1_29	0.35	0.58	0.44	0.41	0.27	0.44	0.46	0.49	0.45	0.25	0.62	0.39	0.52	0.42	0.16	0.28	0.28	0.45	0.54	0.53	0.43	0.38	0.36	0.51	0.42	0.12	0.22	0.44	1	0.38	-0.1	-0.14	0.12	0.14	0.15	-0.05	0.04	0.01	0.06	0.09	0.09	0.1	0	-0.04	-0.01	-0.03	0.09	0.12	-0.02	-0.01	0.06	-0.02	-0.1	0.03	0.17	0.06	0.04	-0.14	0	0.16
PRE1_30	0.32	0.44	0.44	0.28	0.3	0.45	0.4	0.3	0.35	0.32	0.42	0.39	0.38	0.34	0.28	0.33	0.22	0.47	0.49	0.27	0.41	0.29	0.44	0.43	0.21	0.08	0.07	0.26	0.38	1	-0.04	-0.02	0.05	0.01	0.11	0.01	0.02	-0.01	-0.04	0.11	0.04	-0.03	-0.11	0.17	0.03	-0.06	0.03	0.09	-0.07	0.13	0.06	0.02	-0.09	0.08	0.04	0.03	-0.04	0.05	-0.06	0.12
POST1_1	0.13	-0.07	-0.2	-0.08	-0.11	-0.14	-0.13	-0.06	-0.04	0.03	0	-0.05	-0.07	-0.14	-0.07	-0.07	-0.14	-0.12	0.06	-0.07	-0.1	-0.04	-0.1	-0.05	-0.05	-0.04	-0.01	-0.15	-0.1	-0.04	1	0.5	0.21	-0.1	-0.05	0.11	0.33	0.44	0.42	0.35	0.27	0.25	0.44	0.35	0.31	0.45	0.14	0.26	0.47	0.33	0.25	0.51	0.43	0.33	0.12	0.31	0.47	0.42	0.24	0.2
POST1_2	-0.02	-0.01	-0.08	-0.04	-0.13	-0.06	-0.09	-0.08	-0.03	0	-0.04	-0.09	-0.07	-0.03	-0.04	0	-0.11	-0.04	0.01	-0.13	0.01	-0.05	0.01	-0.04	-0.21	0	-0.02	-0.11	-0.14	-0.02	0.5	1	0.37	0.09	-0.11	0.25	0.46	0.55	0.34	0.36	0.44	0.43	0.38	0.37	0.33	0.35	0.37	0.22	0.52	0.49	0.34	0.54	0.41	0.34	0.32	0.35	0.44	0.53	0.4	0.25
POST1_3	-0.13	-0.02	-0.09	0.06	0.06	-0.03	-0.04	-0.07	0.02	0.02	-0.04	-0.13	-0.15	0.06	0.13	0.03	-0.25	0.06	0.04	0	0.04	0	-0.01	-0.06	-0.08	-0.01	-0.18	-0.11	0.12	0.05	0.21	0.37	1	0.34	-0.05	0.45	0.29	0.42	0.31	0.39	0.21	0.47	0.52	0.34	0.32	0.46	0.37	0.36	0.43	0.27	0.2	0.51	0.32	0.46	0.4	0.43	0.51	0.31	0.33	0.31
POST1_4	-0.1	-0.13	-0.02	0.14	0.12	-0.06	0.03	-0.03	0.07	0.01	0.03	-0.04	-0.13	0.09	0.07	0.06	-0.13	-0.01	-0.01	0.11	-0.02	0	0.02	0.05	-0.05	-0.05	-0.1	0.01	0.14	0.01	-0.1	0.09	0.34	1	0.26	0.46	0.38	0.06	0.3	0.32	0.2	0.35	0.35	0.33	0.3	0.1	0.5	0.41	0.22	0.32	0.26	0.34	0.28	0.27	0.37	0.15	0.27	0.35	0.34	0.41
POST1_5	0.04	-0.01	0.06	0.17	0.12	0.02	0.1	0.08	0.06	0.12	0.18	0.11	-0.01	0.1	0.01	0.05	0.07	0.07	0.07	0.13	0.07	0.09	-0.03	0.14	0.11	-0.05	0.02	0.17	0.15	0.11	-0.05	-0.11	-0.05	0.26	1	0.3	0.27	0.07	0.16	0.13	0.24	0.25	0.09	0.22	0.14	0.19	0.3	0.26	0.13	0.07	0.43	0.13	0.16	0.11	0.1	0.18	0.09	0.17	0.18	0.32
POST1_6	0.02	-0.11	-0.08	0.05	0.04	-0.17	-0.02	0	0.09	0.03	-0.11	-0.12	-0.19	0.18	0.13	0.1	-0.12	0.02	-0.07	-0.02	0.09	0.09	-0.03	-0.08	-0.16	-0.04	0.02	-0.04	-0.05	0.01	0.11	0.25	0.45	0.46	0.3	1	0.33	0.04	0.1	0.04	0.13	0.47	0.39	0.34	0.23	0.15	0.29	0.55	0.34	0.29	0.21	0.4	0.36	0.33	0.26	0.33	0.24	0.42	0.22	0.34
POST1_7	0.09	-0.06	-0.02	0.08	-0.07	-0.12	0	0	0.04	0.12	0.1	0.07	-0.12	-0.05	0.05	0.07	-0.13	-0.02	0.06	0.07	0.02	-0.07	0.11	-0.05	0.01	-0.01	0	-0.01	0.04	0.02	0.33	0.46	0.29	0.38	0.27	0.33	1	0.28	0.1	0.08	0.2	0.39	0.3	0.48	0.37	0.29	0.27	0.34	0.41	0.45	0.39	0.31	0.33	0.33	0.38	0.43	0.42	0.23	0.42	0.26
POST1_8	-0.12	0.07	-0.01	0.02	-0.08	-0.03	-0.11	-0.04	-0.02	0.1	0.09	-0.13	-0.03	0.01	-0.04	-0.07	-0.12	0.02	0.07	0	0.01	0.07	0.06	-0.1	-0.14	0.04	-0.1	-0.07	0.01	-0.01	0.44	0.55	0.42	0.06	0.07	0.04	0.28	1	0.09	0.23	0.35	0.38	0.41	0.31	0.15	0.5	0.46	0.09	0.31	0.18	0.41	0.51	0.23	0.24	0.18	0.25	0.4	0.28	0.38	0.28
POST1_9	-0.01	-0.13	-0.21	0.04	0.03	-0.03	-0.07	-0.15	-0.06	0.01	-0.03	-0.13	-0.07	-0.06	-0.01	-0.07	-0.07	-0.03	0	-0.13	-0.08	-0.07	-0.2	0.08	-0.03	-0.07	-0.11	-0.14	0.06	-0.04	0.42	0.34	0.31	0.3	0.16	0.1	0.1	0.09	1	0.25	0.36	0.14	0.41	0.27	0.36	0.25	0.27	0.27	0.41	0.36	0.09	0.48	0.59	0.34	0.06	0.13	0.37	0.49	0.28	0.28
POST1_10	-0.04	0	-0.01	0.05	0.09	0.08	0.05	0.02	0.01	-0.09	0.08	0.1	-0.03	-0.02	-0.04	0.03	-0.13	-0.05	0.13	0.11	-0.03	-0.04	-0.04	0.17	0.02	-0.07	-0.1	0.05	0.09	0.11	0.35	0.36	0.39	0.32	0.13	0.04	0.08	0.23	0.25	1	0.34	0.39	0.3	0.24	0.31	0.4	0.38	0.21	0.34	0.24	0.38	0.35	0.1	0.28	0.46	0.29	0.39	0.38	0.22	0.3
POST1_11	-0.07	-0.05	-0.06	0.04	-0.1	-0.1	-0.13	-0.05	0.02	0.03	0.15	-0.09	0	-0.15	-0.12	-0.2	-0.19	-0.02	0.06	0.11	-0.13	-0.03	-0.06	0.02	-0.03	-0.12	-0.22	-0.02	0.09	0.04	0.27	0.44	0.21	0.2	0.24	0.13	0.2	0.35	0.36	0.34	1	0.32	0.12	0.02	-0.04	0.43	0.3	0.32	0.2	0.13	0.26	0.24	0.38	0.31	0.19	0.13	0.34	0.45	0.17	0.29
POST1_12	0.1	-0.02	0	0.07	-0.1	-0.07	-0.03	-0.07	0.14	0.1	0.1	0.02	-0.1	0.06	-0.02	0.02	-0.09	0.13	-0.08	0.07	0.15	0.02	-0.06	-0.03	-0.01	-0.01	-0.05	0.04	0.1	-0.03	0.25	0.43	0.47	0.35	0.25	0.47	0.39	0.38	0.14	0.39	0.32	1	0.32	0.13	0.01	0.36	0.48	0.26	0.36	0.29	0.43	0.31	0.22	0.4	0.41	0.32	0.31	0.44	0.26	0.43
POST1_13	-0.1	-0.16	-0.17	0.1	-0.06	-0.13	-0.1	-0.09	-0.08	0	-0.06	-0.14	-0.14	-0.02	-0.05	-0.04	-0.31	0.01	-0.03	-0.02	-0.03	-0.17	-0.16	0.02	-0.06	-0.09	-0.1	-0.1	0	-0.11	0.44	0.38	0.52	0.35	0.09	0.39	0.3	0.41	0.41	0.3	0.12	0.32	1	0.19	0.16	0.4	0.44	0.41	0.38	0.19	0.2	0.7	0.39	0.27	0.23	0.27	0.45	0.24	0.48	0.38
POST1_14	-0.01	-0.03	-0.08	-0.04	0.18	-0.02	-0.01	0.01	-0.02	0.04	-0.08	-0.05	-0.06	0.06	0.14	0.01	-0.12	-0.07	0.19	0.01	0.04	0.02	0.06	0.02	-0.13	0.02	-0.04	-0.11	-0.04	0.17	0.35	0.37	0.34	0.33	0.22	0.34	0.48	0.31	0.27	0.24	0.02	0.13	0.19	1	0.26	0.23	0.17	0.23	0.47	0.54	0.35	0.35	0.29	0.42	0.23	0.37	0.4	0.45	0.23	0.18
POST1_15	0.01	0.04	-0.04	0.07	0.09	0.03	0.1	0.03	0.02	-0.01	0.03	0.04	-0.14	0.11	0.13	0.26	0.14	-0.11	0.03	-0.14	-0.03	0.16	0.11	-0.01	-0.07	0.06	0.11	-0.02	-0.01	0.03	0.31	0.33	0.32	0.3	0.14	0.23	0.37	0.15	0.36	0.31	-0.04	0.01	0.16	0.26	1	0.16	0.27	0.27	0.38	0.34	0.22	0.46	0.35	0.13	0.25	0.33	0.31	0.24	0.35	0.19
POST1_16	-0.14	-0.14	-0.08	0.03	-0.12	-0.18	-0.16	-0.1	-0.08	0.08	-0.03	-0.14	-0.12	-0.05	-0.1	-0.11	-0.16	-0.09	-0.05	-0.03	-0.2	-0.01	-0.07	-0.11	-0.07	-0.1	-0.17	-0.1	-0.03	-0.06	0.45	0.35	0.46	0.1	0.19	0.15	0.29	0.5	0.25	0.4	0.43	0.36	0.4	0.23	0.16	1	0.3	0.08	0.11	0.04	0.28	0.4	0.3	0.22	0.37	0.36	0.52	0.29	0.16	0.25
POST1_17	-0.09	-0.09	-0.08	0.1	0.01	-0.06	-0.09	-0.06	0.02	0.06	0.03	-0.05	-0.1	0.08	-0.1	-0.07	-0.18	0.05	0	0.06	0.03	-0.04	-0.06	0.01	-0.08	-0.07	-0.06	-0.13	0.09	0.03	0.14	0.37	0.37	0.5	0.3	0.29	0.27	0.46	0.27	0.38	0.3	0.48	0.44	0.17	0.27	0.3	1	0.2	0.06	0.04	0.35	0.57	0.28	0.06	0.36	0.22	0.21	0.3	0.37	0.56
POST1_18	-0.02	-0.1	0.01	0.14	-0.08	-0.04	-0.04	0.04	0.03	-0.03	0.05	0	-0.12	0	0.04	-0.03	-0.26	0.03	0.09	0.13	0.04	-0.03	-0.14	0.11	0	-0.07	-0.15	-0.02	0.12	0.09	0.26	0.22	0.36	0.41	0.26	0.55	0.34	0.09	0.27	0.21	0.32	0.26	0.41	0.23	0.27	0.08	0.2	1	0.28	0.05	0.18	0.36	0.4	0.37	0.2	0.33	0.36	0.34	0.26	0.21
POST1_19	0.02	0.02	-0.16	-0.02	0.03	-0.1	-0.01	-0.08	0.05	0.04	0.07	-0.05	-0.13	-0.08	0.09	0.05	-0.07	-0.06	0.05	-0.07	0.08	-0.03	-0.02	-0.06	-0.07	-0.05	0.03	0.01	-0.02	-0.07	0.47	0.52	0.43	0.22	0.13	0.34	0.41	0.31	0.41	0.34	0.2	0.36	0.38	0.47	0.38	0.11	0.06	0.28	1	0.39	0.35	0.43	0.36	0.58	0.1	0.39	0.44	0.41	0.35	0.23
POST1_20	0.17	0.07	-0.02	-0.01	0.17	0.12	0.15	0.04	0.06	0	0	0.04	0.03	0.12	0.18	0.24	0.09	0.03	0.09	-0.05	0.07	0.11	0.17	0.09	-0.08	0.15	0.05	0.04	-0.01	0.13	0.33	0.49	0.27	0.32	0.07	0.29	0.45	0.18	0.36	0.24	0.13	0.29	0.19	0.54	0.34	0.04	0.04	0.05	0.39	1	0.29	0.29	0.31	0.34	0.28	0.15	0.31	0.48	0.38	0.2
POST1_21	0.03	0.03	-0.03	0.18	0.03	0.06	0.12	-0.07	0.03	0.11	0	0.04	0.03	0.12	0.04	0.08	0.01	0.06	0.05	0.05	0.04	0.15	0.05	-0.02	0.03	0.11	0.03	-0.02	0.06	0.06	0.25	0.34	0.2	0.26	0.43	0.21	0.39	0.41	0.09	0.38	0.26	0.43	0.2	0.35	0.22	0.28	0.35	0.18	0.35	0.29	1	0.26	0.08	0.02	0.06	0.3	0.27	0.3	0.27	0.32
POST1_22	-0.06	-0.06	-0.19	0.03	0.01	-0.04	-0.08	-0.09	-0.08	0.01	-0.04	-0.13	-0.12	0.01	0	-0.04	-0.22	-0.02	0.06	-0.07	0.01	-0.06	-0.07	-0.02	-0.15	-0.07	-0.01	-0.19	-0.02	0.02	0.51	0.54	0.51	0.34	0.13	0.4	0.31	0.51	0.48	0.35	0.24	0.31	0.7	0.35	0.46	0.4	0.57	0.36	0.43	0.29	0.26	1	0.43	0.18	0.17	0.4	0.49	0.4	0.41	0.37
POST1_23	-0.01	-0.26	-0.25	0.02	0.03	-0.26	-0.07	-0.11	-0.05	0	-0.07	-0.2	-0.21	-0.06	0.04	-0.11	-0.11	-0.16	-0.08	-0.05	-0.04	-0.02	-0.17	-0.11	-0.14	-0.07	-0.15	-0.09	-0.1	-0.09	0.43	0.41	0.32	0.28	0.16	0.36	0.33	0.23	0.59	0.1	0.38	0.22	0.39	0.29	0.35	0.3	0.28	0.4	0.36	0.31	0.08	0.43	1	0.23	-0.1	0.21	0.22	0.45	0.33	0.41
POST1_24	-0.03	0	0.05	-0.07	-0.08	-0.08	-0.08	-0.11	0.1	0.07	0.08	-0.03	-0.09	-0.11	0.04	0.05	-0.14	0	0.02	-0.04	0	-0.09	-0.01	0.04	-0.06	-0.11	-0.14	0.02	0.03	0.08	0.33	0.34	0.46	0.27	0.11	0.33	0.33	0.24	0.34	0.28	0.31	0.4	0.27	0.42	0.13	0.22	0.06	0.37	0.58	0.34	0.02	0.18	0.23	1	0.17	0.26	0.4	0.4	0.23	0.24
POST1_25	0	0.07	0.08	0.06	0.02	0.03	-0.05	0.2	0.07	-0.03	0.15	0.11	-0.06	0.09	-0.03	0.08	-0.12	0.06	0.11	0.11	-0.01	0	0.07	0.14	0.03	0	-0.04	0.08	0.17	0.04	0.12	0.32	0.4	0.37	0.1	0.26	0.38	0.18	0.06	0.46	0.19	0.41	0.23	0.23	0.25	0.37	0.36	0.2	0.1	0.28	0.06	0.17	-0.1	0.17	1	0.24	0.42	0.28	0.26	0.12
POST1_26	-0.1	-0.02	0.01	0.02	0.04	-0.08	-0.03	-0.04	0.04	0.09	-0.01	-0.13	-0.11	0.09	0.12	0.13	-0.17	0.11	-0.05	-0.04	0.07	-0.06	-0.02	-0.03	0.01	-0.05	-0.03	-0.05	0.06	0.03	0.31	0.35	0.43	0.15	0.18	0.33	0.43	0.25	0.13	0.29	0.13	0.32	0.27	0.37	0.33	0.36	0.22	0.33	0.39	0.15	0.3	0.4	0.21	0.26	0.24	1	0.39	0.11	-0.03	-0.03
POST1_27	0.01	0.05	-0.09	0.02	-0.06	-0.1	-0.11	-0.03	0.11	0.09	0.11	-0.04	-0.11	-0.04	0.04	-0.05	-0.17	-0.06	0.14	0.09	-0.07	0.04	0.02	-0.04	-0.01	0.01	-0.02	-0.04	0.04	-0.04	0.47	0.44	0.51	0.27	0.09	0.24	0.42	0.4	0.37	0.39	0.34	0.31	0.45	0.4	0.31	0.52	0.21	0.36	0.44	0.31	0.27	0.49	0.22	0.4	0.42	0.39	1	0.38	0.09	-0.03
POST1_28	-0.04	-0.12	-0.24	-0.04	0.06	-0.11	-0.1	-0.13	-0.02	-0.04	-0.11	-0.07	-0.16	0	-0.06	-0.06	-0.15	-0.12	0.02	-0.1	-0.06	0.04	-0.13	-0.07	-0.17	-0.06	-0.17	-0.1	-0.14	0.05	0.42	0.53	0.31	0.35	0.17	0.42	0.23	0.28	0.49	0.38	0.45	0.44	0.24	0.45	0.24	0.29	0.3	0.34	0.41	0.48	0.3	0.4	0.45	0.4	0.28	0.11	0.38	1	0.15	0.18
POST1_29	-0.01	-0.11	0.03	0.02	-0.09	0.05	0.06	0.02	-0.23	-0.08	0	-0.08	-0.02	-0.01	-0.05	0.04	-0.12	0.02	-0.06	-0.04	-0.02	-0.14	-0.01	0.09	-0.08	0.02	-0.03	-0.09	0	-0.06	0.24	0.4	0.33	0.34	0.18	0.22	0.42	0.38	0.28	0.22	0.17	0.26	0.48	0.23	0.35	0.16	0.37	0.26	0.35	0.38	0.27	0.41	0.33	0.23	0.26	-0.03	0.09	0.15	1	0.31
POST1_30	0.05	-0.04	-0.05	0.21	0.07	-0.03	0.02	0.01	0.15	0.1	0.12	0.1	-0.04	0.03	0.04	0	0.03	-0.01	0.11	0.11	0.09	0.11	0.02	0.07	-0.06	-0.05	-0.04	0.06	0.16	0.12	0.2	0.25	0.31	0.41	0.32	0.34	0.26	0.28	0.28	0.3	0.29	0.43	0.38	0.18	0.19	0.25	0.56	0.21	0.23	0.2	0.32	0.37	0.41	0.24	0.12	-0.03	-0.03	0.18	0.31	1

# mittleres Cronbach´s Alpha zwischen Pre-MZP und Post-MZP:
PRE_alpha = CronbachAlpha(EMA_30.30[pre_30mzp])
POST_alpha = CronbachAlpha(EMA_30.30[post_30mzp])
EMA_30.30_Alpha = FisherZInv(mean(c(FisherZ(PRE_alpha), FisherZ(POST_alpha))))

Korrelation zwischen den Pre- und Post-Intervall-Mittelwerten = -0.046.
Durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden Pre-MZP (Fisher-Z-transformiert): r = 0.38.
Durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden Post-MZP (Fisher-Z-transformiert): r = 0.29.
Mittleres Cronbach´s Alpha zwischen Pre-MZP und Post-MZP = 0.937.

1.4.3 EMA_5.5_Window (je 5 MZP)

# Korrelationsmatrix von PRE- und POST-MZP:
EMA_5.5_Window_KorMat = cor(EMA_5.5_Window[, c(pre_5mzp, post_5mzp)]) %>% 
  round(., digits = 2)

# durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden MZP (beachte: ohne Fisher-Z-Transformation):
pre_inter_item_rtt = 0L
for (i in 1:4) {
  pre_inter_item_rtt = pre_inter_item_rtt + FisherZ(EMA_5.5_Window_KorMat[i,i+1])
}
pre_inter_item_rtt = FisherZInv(pre_inter_item_rtt / 4)

post_inter_item_rtt = 0L
for (i in 5:9) {
  post_inter_item_rtt = post_inter_item_rtt + FisherZ(EMA_5.5_Window_KorMat[i,i+1])
}
post_inter_item_rtt = FisherZInv(post_inter_item_rtt / 4)


for (i in 1:9) {
  EMA_5.5_Window_KorMat[i, i+1] = cell_spec(EMA_5.5_Window_KorMat[i, i+1], "html", bold = TRUE)
}

rownames(EMA_5.5_Window_KorMat) = cell_spec(rownames(EMA_5.5_Window_KorMat), "html", bold = TRUE)

EMA_5.5_Window_KorMat %>%
  kable(., format = "html", escape = FALSE) %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
                full_width = FALSE, fixed_thead = T)

	PRE1_1	PRE1_2	PRE1_3	PRE1_4	PRE1_5	POST1_1	POST1_2	POST1_3	POST1_4	POST1_5
PRE1_1	1	0.38	0.39	0.43	0.36	-0.14	-0.12	0.04	0	-0.04
PRE1_2	0.38	1	0.34	0.12	0.2	-0.01	-0.04	-0.01	0	-0.06
PRE1_3	0.39	0.34	1	0.4	0.21	-0.15	0.06	0.06	-0.06	0.05
PRE1_4	0.43	0.12	0.4	1	0.26	-0.19	-0.04	0.03	-0.06	-0.04
PRE1_5	0.36	0.2	0.21	0.26	1	-0.02	0.03	0.08	0.29	0.02
POST1_1	-0.14	-0.01	-0.15	-0.19	-0.02	1	0.37	0.07	0.17	0.25
POST1_2	-0.12	-0.04	0.06	-0.04	0.03	0.37	1	0.19	0.23	0.31
POST1_3	0.04	-0.01	0.06	0.03	0.08	0.07	0.19	1	0.35	0.22
POST1_4	0	0	-0.06	-0.06	0.29	0.17	0.23	0.35	1	0.28
POST1_5	-0.04	-0.06	0.05	-0.04	0.02	0.25	0.31	0.22	0.28	1

# mittleres Cronbach´s Alpha zwischen Pre-MZP und Post-MZP:
PRE_alpha = CronbachAlpha(EMA_5.5_Window[pre_5mzp])
POST_alpha = CronbachAlpha(EMA_5.5_Window[post_5mzp])
EMA_5.5_Window_Alpha = FisherZInv(mean(c(FisherZ(PRE_alpha), FisherZ(POST_alpha))))

Korrelation zwischen den Pre- und Post-Intervall-Mittelwerten = -0.033.
Durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden Pre-MZP (Fisher-Z-transformiert): r = 0.35.
Durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden Post-MZP (Fisher-Z-transformiert): r = 0.29.
Mittleres Cronbach´s Alpha zwischen Pre-MZP und Post-MZP = 0.655.

1.4.4 EMA_5.5_Days (je 5 MZP)

# Korrelationsmatrix von PRE- und POST-MZP:
EMA_5.5_Days_KorMat = cor(EMA_5.5_Days[, c(pre_5mzp, post_5mzp)]) %>% 
  round(., digits = 2)

# durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden MZP (beachte: ohne Fisher-Z-Transformation):
pre_inter_item_rtt = 0L
for (i in 1:4) {
  pre_inter_item_rtt = pre_inter_item_rtt + FisherZ(EMA_5.5_Days_KorMat[i,i+1])
}
pre_inter_item_rtt = FisherZInv(pre_inter_item_rtt / 4)

post_inter_item_rtt = 0L
for (i in 5:9) {
  post_inter_item_rtt = post_inter_item_rtt + FisherZ(EMA_5.5_Days_KorMat[i,i+1])
}
post_inter_item_rtt = FisherZInv(post_inter_item_rtt / 4)


for (i in 1:9) {
  EMA_5.5_Days_KorMat[i, i+1] = cell_spec(EMA_5.5_Days_KorMat[i, i+1], "html", bold = TRUE)
}

rownames(EMA_5.5_Days_KorMat) = cell_spec(rownames(EMA_5.5_Days_KorMat), "html", bold = TRUE)

EMA_5.5_Days_KorMat %>%
  kable(., format = "html", escape = FALSE) %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
                full_width = FALSE, fixed_thead = T)

	PRE1_1	PRE1_2	PRE1_3	PRE1_4	PRE1_5	POST1_1	POST1_2	POST1_3	POST1_4	POST1_5
PRE1_1	1	0.28	0.56	0.3	0.36	-0.08	-0.06	-0.04	-0.15	-0.04
PRE1_2	0.28	1	0.35	0.41	0.33	0.11	0.12	-0.01	-0.02	0.08
PRE1_3	0.56	0.35	1	0.35	0.44	0.07	-0.03	-0.12	-0.16	-0.08
PRE1_4	0.3	0.41	0.35	1	0.27	-0.13	0.02	0.01	-0.24	0
PRE1_5	0.36	0.33	0.44	0.27	1	0.04	0.03	-0.2	0	-0.02
POST1_1	-0.08	0.11	0.07	-0.13	0.04	1	0.11	-0.01	0.53	0.15
POST1_2	-0.06	0.12	-0.03	0.02	0.03	0.11	1	0.34	0.41	0.39
POST1_3	-0.04	-0.01	-0.12	0.01	-0.2	-0.01	0.34	1	0.21	0.31
POST1_4	-0.15	-0.02	-0.16	-0.24	0	0.53	0.41	0.21	1	0.26
POST1_5	-0.04	0.08	-0.08	0	-0.02	0.15	0.39	0.31	0.26	1

# mittleres Cronbach´s Alpha zwischen Pre-MZP und Post-MZP:
PRE_alpha = CronbachAlpha(EMA_5.5_Days[pre_5mzp])
POST_alpha = CronbachAlpha(EMA_5.5_Days[post_5mzp])
EMA_5.5_Days_Alpha = FisherZInv(mean(c(FisherZ(PRE_alpha), FisherZ(POST_alpha))))

Korrelation zwischen den Pre- und Post-Intervall-Mittelwerten = -0.069.
Durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden Pre-MZP (Fisher-Z-transformiert): r = 0.31.
Durchschnittliche paarweise Korrelation zwischen aufeinanderfolgenden Post-MZP (Fisher-Z-transformiert): r = 0.24.
Mittleres Cronbach´s Alpha zwischen Pre-MZP und Post-MZP = 0.697.

1.5 Pre-Post-Differenz

Verteilungen der Pre-Post-Mittelwerts-Veränderungen

temp = tibble(MeanDiffs = c(EMA_5.5$MeanDiff, EMA_30.30$MeanDiff, EMA_5.5_Window$MeanDiff, EMA_5.5_Days$MeanDiff),
              Datasets = rep(c("EMA_5.5", "EMA_30.30", "EMA_5.5_Window", "EMA_5.5_Days"), each = length(EMA_5.5$MeanDiff)))

temp %>%
  ggplot(aes(x = MeanDiffs, fill = Datasets)) +
    geom_histogram(alpha = 0.2, binwidth = 1, position = "identity") +
    labs(title = "Pre-Post-Differences", x = "PHQ-9 Pre-Post-Difference")

#scatter.hist(EMA_5.5$MeanDiff, EMA_30.30$MeanDiff, xlab = "EMA_5.5$MeanDiff",
#  ylab = "EMA_30.30$MeanDiff", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

#scatter.hist(EMA_5.5$MeanDiff, EMA_5.5_Window$MeanDiff, xlab = "EMA_5.5$MeanDiff",
#  ylab = "EMA_5.5_Window$MeanDiff", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

#scatter.hist(EMA_5.5$MeanDiff, EMA_5.5_Days$MeanDiff, xlab = "EMA_5.5$MeanDiff",
#  ylab = "EMA_5.5_Days$MeanDiff", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

#scatter.hist(EMA_5.5_Window$MeanDiff, EMA_5.5_Days$MeanDiff, xlab = "EMA_5.5_Window$MeanDiff",
#  ylab = "EMA_5.5_Days$MeanDiff", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

Korrelation zwischen den Pre-Post-Differenzen in EMA_5.5 und EMA_30.30 = 1.
Korrelation zwischen den Pre-Post-Differenzen in EMA_5.5_Window und EMA_30.30 = 0.907.
Korrelation zwischen den Pre-Post-Differenzen in EMA_5.5_Days und EMA_30.30 = 0.887.

Prozentuale Überlappung der Pre-Post-Mittelwerts-Veränderungen

# Overlap-Plots zum Vergleich
final.plot(list(EMA_5.5_MeanDiff = EMA_5.5$MeanDiff, EMA_30.30_MeanDiff = EMA_30.30$MeanDiff), 
           overlap(list(EMA_5.5_MeanDiff = EMA_5.5$MeanDiff, EMA_30.30_MeanDiff = EMA_30.30$MeanDiff))$OV)

final.plot(list(EMA_5.5_Window_MeanDiff = EMA_5.5_Window$MeanDiff, EMA_30.30_MeanDiff = EMA_30.30$MeanDiff), 
           overlap(list(EMA_5.5_Window_MeanDiff = EMA_5.5_Window$MeanDiff, EMA_30.30_MeanDiff = EMA_30.30$MeanDiff))$OV)

final.plot(list(EMA_5.5_Days_MeanDiff = EMA_5.5_Days$MeanDiff, EMA_30.30_MeanDiff = EMA_30.30$MeanDiff), 
           overlap(list(EMA_5.5_Days_MeanDiff = EMA_5.5_Days$MeanDiff, EMA_30.30_MeanDiff = EMA_30.30$MeanDiff))$OV)

final.plot(list(EMA_5.5_Window_MeanDiff = EMA_5.5_Window$MeanDiff, EMA_5.5_Days_MeanDiff = EMA_5.5_Days$MeanDiff), 
           overlap(list(EMA_5.5_Window_MeanDiff = EMA_5.5_Window$MeanDiff, EMA_5.5_Days_MeanDiff = EMA_5.5_Days$MeanDiff))$OV)

1.5.1 Cohen´s d

Cohen´s d (mit gepoolten SDs) vom Pre- zum Post-Intervall in EMA_5.5 (je 5 MZP)

\[ d = \frac{\overline{x_{1}} - \overline{x_{2}}} {\sqrt{0.5 \cdot (s_{x}^2 + s_{y}^2)}} \]

\(\overline{x_{1}}\) = mean of subject´s pretest scores, \(\overline{x_{2}}\) = mean of subject´s posttest scores, \(s_{x}\) = individual standard deviation of pretest time points, \(s_{y}\) = individual standard deviation of posttest time points

EMA_5.5$Cohen_d = (EMA_5.5$PRE_Mean - EMA_5.5$POST_Mean) / sqrt(0.5 * (EMA_5.5$ind.pretestSD^2 + EMA_5.5$ind.posttestSD^2))

# Sollen Cohen_d %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_5.5 = EMA_5.5 %>% 
#  within(., {Cohen_d[Cohen_d %in% c(-Inf,Inf)] = NA})

#hist(EMA_5.5$Cohen_d, col = "lightblue1", main = "EMA_5.5$Cohen_d")

cohen_d_5.5 = (mean(EMA_5.5$PRE_Mean) - mean(EMA_5.5$POST_Mean)) / sqrt(0.5 * (mean(EMA_5.5$ind.pretestSD)^2 +
  mean(EMA_5.5$ind.posttestSD)^2))

final.plot(list(EMA_5.5_PRE_Mean = EMA_5.5$PRE_Mean, EMA_5.5_POST_Mean = EMA_5.5$POST_Mean), 
           overlap(list(EMA_5.5_PRE_Mean = EMA_5.5$PRE_Mean, EMA_5.5_POST_Mean = EMA_5.5$POST_Mean))$OV)

Gepoolte Varianz zwischen Pre- und Post-Intervall-Mittelwerten in EMA_5.5 = 3.09.
Durchschnittliches Cohen´s d zwischen Pre- und Post-Mittelwerten (für jede Person einzeln berechnet) in EMA_5.5 = 1.129.
Durchschnittliches Cohen´s d zwischen Pre- und Post-Mittelwerten in EMA_5.5 = 0.991.

Cohen´s d (mit gepoolten SDs) vom Pre- zum Post-Intervall in den erweiterten Intervall-Daten (je 30 MZP)

EMA_30.30$Cohen_d = (EMA_30.30$PRE_Mean - EMA_30.30$POST_Mean) / sqrt(0.5 * (EMA_30.30$ind.pretestSD^2 + EMA_30.30$ind.posttestSD^2))

# Sollen Cohen_d %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_30.30 = EMA_30.30 %>% 
#  within(., {Cohen_d[Cohen_d %in% c(-Inf,Inf)] = NA})

#hist(EMA_30.30$Cohen_d, col = "lightblue1", main = "EMA_30.30$Cohen_d")

cohen_d_30.30 = (mean(EMA_30.30$PRE_Mean) - mean(EMA_30.30$POST_Mean)) / sqrt(0.5 * (mean(EMA_30.30$ind.pretestSD)^2 +
  mean(EMA_30.30$ind.posttestSD)^2))

final.plot(list(EMA_30.30_PRE_Mean = EMA_30.30$PRE_Mean, EMA_30.30_POST_Mean = EMA_30.30$POST_Mean), 
           overlap(list(EMA_30.30_PRE_Mean = EMA_30.30$PRE_Mean, EMA_30.30_POST_Mean = EMA_30.30$POST_Mean))$OV)

Gepoolte Varianz zwischen Pre- und Post-Intervall-Mittelwerten in EMA_30.30 = 3.09.
Durchschnittliches Cohen´s d zwischen Pre- und Post-Mittelwerten (für jede Person einzeln berechnet) in EMA_30.30 = 1.241.
Durchschnittliches Cohen´s d zwischen Pre- und Post-Mittelwerten in EMA_30.30 = 1.089.

Cohen´s d (mit gepoolten SDs) vom Pre- zum Post-Intervall in EMA_5.5_Window (je 5 MZP)

EMA_5.5_Window$Cohen_d = (EMA_5.5_Window$PRE_Mean - EMA_5.5_Window$POST_Mean) / sqrt(0.5 * (EMA_5.5_Window$ind.pretestSD^2 + EMA_5.5_Window$ind.posttestSD^2))

# Sollen Cohen_d %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_5.5_Window = EMA_5.5_Window %>% 
#  within(., {Cohen_d[Cohen_d %in% c(-Inf,Inf)] = NA})

#hist(EMA_5.5_Window$Cohen_d, col = "lightblue1", main = "EMA_5.5_Window$Cohen_d")

cohen_d_5.5_Window = (mean(EMA_5.5_Window$PRE_Mean) - mean(EMA_5.5_Window$POST_Mean)) / sqrt(0.5 * (mean(EMA_5.5_Window$ind.pretestSD)^2 + mean(EMA_5.5_Window$ind.posttestSD)^2))

final.plot(list(EMA_5.5_Window_PRE_Mean = EMA_5.5_Window$PRE_Mean, EMA_5.5_Window_POST_Mean = EMA_5.5_Window$POST_Mean),
    overlap(list(EMA_5.5_Window_PRE_Mean = EMA_5.5_Window$PRE_Mean, EMA_5.5_Window_POST_Mean = EMA_5.5_Window$POST_Mean))$OV)

Gepoolte Varianz zwischen Pre- und Post-Intervall-Mittelwerten in EMA_5.5_Window = 3.379.
Durchschnittliches Cohen´s d zwischen Pre- und Post-Mittelwerten (für jede Person einzeln berechnet) in EMA_5.5_Window = 1.215.
Durchschnittliches Cohen´s d zwischen Pre- und Post-Mittelwerten in EMA_5.5_Window = 1.025.

Cohen´s d (mit gepoolten SDs) vom Pre- zum Post-Intervall in EMA_5.5_Days (je 5 MZP)

EMA_5.5_Days$Cohen_d = (EMA_5.5_Days$PRE_Mean - EMA_5.5_Days$POST_Mean) / sqrt(0.5 * (EMA_5.5_Days$ind.pretestSD^2 + EMA_5.5_Days$ind.posttestSD^2))

# Sollen Cohen_d %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_5.5_Days = EMA_5.5_Days %>% 
#  within(., {Cohen_d[Cohen_d %in% c(-Inf,Inf)] = NA})

#hist(EMA_5.5_Days$Cohen_d, col = "lightblue1", main = "EMA_5.5_Days$Cohen_d")

cohen_d_5.5_Days = (mean(EMA_5.5_Days$PRE_Mean) - mean(EMA_5.5_Days$POST_Mean)) / sqrt(0.5 * (mean(EMA_5.5_Days$ind.pretestSD)^2 + mean(EMA_5.5_Days$ind.posttestSD)^2))

final.plot(list(EMA_5.5_Days_PRE_Mean = EMA_5.5_Days$PRE_Mean, EMA_5.5_Days_POST_Mean = EMA_5.5_Days$POST_Mean),
    overlap(list(EMA_5.5_Days_PRE_Mean = EMA_5.5_Days$PRE_Mean, EMA_5.5_Days_POST_Mean = EMA_5.5_Days$POST_Mean))$OV)

Gepoolte Varianz zwischen Pre- und Post-Intervall-Mittelwerten in EMA_5.5_Days = 3.435.
Durchschnittliches Cohen´s d zwischen Pre- und Post-Mittelwerten (für jede Person einzeln berechnet) in EMA_5.5_Days = 1.399.
Durchschnittliches Cohen´s d zwischen Pre- und Post-Mittelwerten in EMA_5.5_Days = 1.166.

Ab hier nur noch Vergleiche in EMA_30.30, EMA_5.5_Window und EMA_5.5_Days:

1.6 Klinische PHQ-9-Interpretation

PHQ_Int = tibble(PHQ_Score = c("0-4","5-9","10-14","15-19","20-27"),
       Klassifikation = c(0,1,2,3,4),
       Interpretation = c("Minimal or none","Mild","Moderate","Moderately severe","Severe"))

1.6.1 EMA_30.30

EMA_30.30 = EMA_30.30 %>% 
  mutate(PRE_Mean_klass = case_when(
    PRE_Mean <= 4 ~ 0,
    PRE_Mean > 4 & PRE_Mean < 10 ~ 1,
    PRE_Mean >= 10 & PRE_Mean < 15 ~ 2,
    PRE_Mean >= 15 & PRE_Mean < 20 ~ 3,
    PRE_Mean >= 20 ~ 4,
    TRUE ~ PRE_Mean
  )
)

temp = EMA_30.30 %>% 
  count(PRE_Mean_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

PHQ_Int %>%
  dplyr::rename(PRE_Mean_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

PHQ_Score	PRE_Mean_klass	Interpretation	n	Percentage
0-4	0	Minimal or none	NA	NA
5-9	1	Mild	40	40
10-14	2	Moderate	60	60
15-19	3	Moderately severe	NA	NA
20-27	4	Severe	NA	NA

EMA_30.30 = EMA_30.30 %>% 
  mutate(POST_Mean_klass = case_when(
    POST_Mean <= 4 ~ 0,
    POST_Mean > 4 & POST_Mean < 10 ~ 1,
    POST_Mean >= 10 & POST_Mean < 15 ~ 2,
    POST_Mean >= 15 & POST_Mean < 20 ~ 3,
    POST_Mean >= 20 ~ 4,
    TRUE ~ POST_Mean
  )
)

temp = EMA_30.30 %>% 
  count(POST_Mean_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

PHQ_Int %>%
  dplyr::rename(POST_Mean_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

PHQ_Score	POST_Mean_klass	Interpretation	n	Percentage
0-4	0	Minimal or none	8	8
5-9	1	Mild	73	73
10-14	2	Moderate	19	19
15-19	3	Moderately severe	NA	NA
20-27	4	Severe	NA	NA

temp = tibble(Klassifikation = c(EMA_30.30$PRE_Mean_klass, EMA_30.30$POST_Mean_klass),
              MZP = rep(c("PRE_Mean_klass", "POST_Mean_klass"), each = length(EMA_30.30$PRE_Mean_klass)))

temp %>%
  ggplot(aes(x = Klassifikation, fill = MZP)) +
    geom_histogram(alpha = 0.2, binwidth = 1, position = "identity") +
    labs(title = "EMA_30.30: PHQ-9 Classification", x = "Classification")

1.6.2 EMA_5.5_Window

EMA_5.5_Window = EMA_5.5_Window %>% 
  mutate(PRE_Mean_klass = case_when(
    PRE_Mean <= 4 ~ 0,
    PRE_Mean > 4 & PRE_Mean < 10 ~ 1,
    PRE_Mean >= 10 & PRE_Mean < 15 ~ 2,
    PRE_Mean >= 15 & PRE_Mean < 20 ~ 3,
    PRE_Mean >= 20 ~ 4,
    TRUE ~ PRE_Mean
  )
)

temp = EMA_5.5_Window %>% 
  count(PRE_Mean_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

PHQ_Int %>%
  dplyr::rename(PRE_Mean_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

PHQ_Score	PRE_Mean_klass	Interpretation	n	Percentage
0-4	0	Minimal or none	NA	NA
5-9	1	Mild	41	41
10-14	2	Moderate	57	57
15-19	3	Moderately severe	2	2
20-27	4	Severe	NA	NA

EMA_5.5_Window = EMA_5.5_Window %>% 
  mutate(POST_Mean_klass = case_when(
    POST_Mean <= 4 ~ 0,
    POST_Mean > 4 & POST_Mean < 10 ~ 1,
    POST_Mean >= 10 & POST_Mean < 15 ~ 2,
    POST_Mean >= 15 & POST_Mean < 20 ~ 3,
    POST_Mean >= 20 ~ 4,
    TRUE ~ POST_Mean
  )
)

temp = EMA_5.5_Window %>% 
  count(POST_Mean_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

PHQ_Int %>%
  dplyr::rename(POST_Mean_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

PHQ_Score	POST_Mean_klass	Interpretation	n	Percentage
0-4	0	Minimal or none	8	8
5-9	1	Mild	70	70
10-14	2	Moderate	22	22
15-19	3	Moderately severe	NA	NA
20-27	4	Severe	NA	NA

temp = tibble(Klassifikation = c(EMA_5.5_Window$PRE_Mean_klass, EMA_5.5_Window$POST_Mean_klass),
              MZP = rep(c("PRE_Mean_klass", "POST_Mean_klass"), each = length(EMA_5.5_Window$PRE_Mean_klass)))

temp %>%
  ggplot(aes(x = Klassifikation, fill = MZP)) +
    geom_histogram(alpha = 0.2, binwidth = 1, position = "identity") +
    labs(title = "EMA_5.5_Window: PHQ-9 Classification", x = "Classification")

1.6.3 EMA_5.5_Days

EMA_5.5_Days = EMA_5.5_Days %>% 
  mutate(PRE_Mean_klass = case_when(
    PRE_Mean <= 4 ~ 0,
    PRE_Mean > 4 & PRE_Mean < 10 ~ 1,
    PRE_Mean >= 10 & PRE_Mean < 15 ~ 2,
    PRE_Mean >= 15 & PRE_Mean < 20 ~ 3,
    PRE_Mean >= 20 ~ 4,
    TRUE ~ PRE_Mean
  )
)

temp = EMA_5.5_Days %>% 
  count(PRE_Mean_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

PHQ_Int %>%
  dplyr::rename(PRE_Mean_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

PHQ_Score	PRE_Mean_klass	Interpretation	n	Percentage
0-4	0	Minimal or none	NA	NA
5-9	1	Mild	41	41
10-14	2	Moderate	58	58
15-19	3	Moderately severe	1	1
20-27	4	Severe	NA	NA

EMA_5.5_Days = EMA_5.5_Days %>% 
  mutate(POST_Mean_klass = case_when(
    POST_Mean <= 4 ~ 0,
    POST_Mean > 4 & POST_Mean < 10 ~ 1,
    POST_Mean >= 10 & POST_Mean < 15 ~ 2,
    POST_Mean >= 15 & POST_Mean < 20 ~ 3,
    POST_Mean >= 20 ~ 4,
    TRUE ~ POST_Mean
  )
)

temp = EMA_5.5_Days %>% 
  count(POST_Mean_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

PHQ_Int %>%
  dplyr::rename(POST_Mean_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

PHQ_Score	POST_Mean_klass	Interpretation	n	Percentage
0-4	0	Minimal or none	11	11
5-9	1	Mild	71	71
10-14	2	Moderate	18	18
15-19	3	Moderately severe	NA	NA
20-27	4	Severe	NA	NA

temp = tibble(Klassifikation = c(EMA_5.5_Days$PRE_Mean_klass, EMA_5.5_Days$POST_Mean_klass),
              MZP = rep(c("PRE_Mean_klass", "POST_Mean_klass"), each = length(EMA_5.5_Days$PRE_Mean_klass)))

temp %>%
  ggplot(aes(x = Klassifikation, fill = MZP)) +
    geom_histogram(alpha = 0.2, binwidth = 1, position = "identity") +
    labs(title = "EMA_5.5_Days: PHQ-9 Classification", x = "Classification")

1.7 Percentage Change (PC)

\[ PC = \Bigl(1 - \frac{\overline{x_{2}}} {\overline{x_{1}}}\Bigr) \cdot 100 \]

\(\overline{x_{2}}\) = mean of subject´s posttest scores, \(\overline{x_{1}}\) = mean of subject´s pretest scores

Interpretation des Percentage Change:

PC_Int = tibble(PC = c("PC <= -50","-50 < PC <= -25","-25 < PC < 25","25 <= PC < 50","PC >= 50"),
                Klassifikation = c(-2,-1,0,1,2),
                Interpretation = c("starke Verschlechterung","Verschlechterung","keine Veränderung",
                                   "Verbesserung","starke Verbesserung"))

1.7.1 EMA_30.30

EMA_30.30$Mean_PC = (1-(EMA_30.30$POST_Mean / EMA_30.30$PRE_Mean)) * 100

# Sollen Mean_PC %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_30.30 = EMA_30.30 %>% 
#  within(., {Mean_PC[Mean_PC %in% c(-Inf,Inf)] = NA})

EMA_30.30 = EMA_30.30 %>% 
  mutate(Mean_PC_klass = case_when(
    Mean_PC <= -50 ~ -2,
    Mean_PC > -50 & Mean_PC <= -25 ~ -1,
    Mean_PC > -25 & Mean_PC < 25 ~ 0,
    Mean_PC >= 25 & Mean_PC < 50 ~ 1,
    Mean_PC >= 50 ~ 2,
    TRUE ~ Mean_PC
  )
)


temp = EMA_30.30 %>% 
  dplyr::count(Mean_PC_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

PC_Int %>%
  dplyr::rename(Mean_PC_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

PC	Mean_PC_klass	Interpretation	n	Percentage
PC <= -50	-2	starke Verschlechterung	NA	NA
-50 < PC <= -25	-1	Verschlechterung	4	4
-25 < PC < 25	0	keine Veränderung	43	43
25 <= PC < 50	1	Verbesserung	30	30
PC >= 50	2	starke Verbesserung	23	23

scatter.hist(EMA_30.30$PRE_Mean, EMA_30.30$Mean_PC, xlab = "EMA_30.30$PRE_Mean", ylab = "EMA_30.30$Mean_PC", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

Korrelation Mean Percentage Change (je 30 MZP) mit PHQ-Baseline (Pre-Intervall-Mean) = 0.533.

1.7.2 EMA_5.5_Window

EMA_5.5_Window$Mean_PC = (1-(EMA_5.5_Window$POST_Mean / EMA_5.5_Window$PRE_Mean)) * 100

# Sollen Mean_PC %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_5.5_Window = EMA_5.5_Window %>% 
#  within(., {Mean_PC[Mean_PC %in% c(-Inf,Inf)] = NA})

EMA_5.5_Window = EMA_5.5_Window %>% 
  mutate(Mean_PC_klass = case_when(
    Mean_PC <= -50 ~ -2,
    Mean_PC > -50 & Mean_PC <= -25 ~ -1,
    Mean_PC > -25 & Mean_PC < 25 ~ 0,
    Mean_PC >= 25 & Mean_PC < 50 ~ 1,
    Mean_PC >= 50 ~ 2,
    TRUE ~ Mean_PC
  )
)


temp = EMA_5.5_Window %>% 
  dplyr::count(Mean_PC_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

PC_Int %>%
  dplyr::rename(Mean_PC_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

PC	Mean_PC_klass	Interpretation	n	Percentage
PC <= -50	-2	starke Verschlechterung	2	2
-50 < PC <= -25	-1	Verschlechterung	4	4
-25 < PC < 25	0	keine Veränderung	43	43
25 <= PC < 50	1	Verbesserung	25	25
PC >= 50	2	starke Verbesserung	26	26

scatter.hist(EMA_5.5_Window$PRE_Mean, EMA_5.5_Window$Mean_PC, xlab = "EMA_5.5_Window$PRE_Mean", ylab = "EMA_5.5_Window$Mean_PC", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

Korrelation Mean Percentage Change (je 5 MZP) mit PHQ-Baseline (Pre-Intervall-Mean) = 0.528.

1.7.3 EMA_5.5_Days

EMA_5.5_Days$Mean_PC = (1-(EMA_5.5_Days$POST_Mean / EMA_5.5_Days$PRE_Mean)) * 100

# Sollen Mean_PC %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_5.5_Days = EMA_5.5_Days %>% 
#  within(., {Mean_PC[Mean_PC %in% c(-Inf,Inf)] = NA})

EMA_5.5_Days = EMA_5.5_Days %>% 
  mutate(Mean_PC_klass = case_when(
    Mean_PC <= -50 ~ -2,
    Mean_PC > -50 & Mean_PC <= -25 ~ -1,
    Mean_PC > -25 & Mean_PC < 25 ~ 0,
    Mean_PC >= 25 & Mean_PC < 50 ~ 1,
    Mean_PC >= 50 ~ 2,
    TRUE ~ Mean_PC
  )
)


temp = EMA_5.5_Days %>% 
  dplyr::count(Mean_PC_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

PC_Int %>%
  dplyr::rename(Mean_PC_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

PC	Mean_PC_klass	Interpretation	n	Percentage
PC <= -50	-2	starke Verschlechterung	2	2
-50 < PC <= -25	-1	Verschlechterung	8	8
-25 < PC < 25	0	keine Veränderung	32	32
25 <= PC < 50	1	Verbesserung	29	29
PC >= 50	2	starke Verbesserung	29	29

scatter.hist(EMA_5.5_Days$PRE_Mean, EMA_5.5_Days$Mean_PC, xlab = "EMA_5.5_Days$PRE_Mean", ylab = "EMA_5.5_Days$Mean_PC", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

Korrelation Mean Percentage Change (je 5 MZP) mit PHQ-Baseline (Pre-Intervall-Mean) = 0.545.

1.7.4 Zusammenhang im Scatter-Histogramm

scatter.hist(EMA_30.30$Mean_PC, EMA_5.5_Window$Mean_PC, xlab = "EMA_30.30$Mean_PC", ylab = "EMA_5.5_Window$Mean_PC", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

scatter.hist(EMA_30.30$Mean_PC, EMA_5.5_Days$Mean_PC, xlab = "EMA_30.30$Mean_PC", ylab = "EMA_5.5_Days$Mean_PC", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

scatter.hist(EMA_5.5_Window$Mean_PC, EMA_5.5_Days$Mean_PC, xlab = "EMA_5.5_Window$Mean_PC", ylab = "EMA_5.5_Days$Mean_PC", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

1.8 Individual Reliable Change Index (ind)

1.8.1 RCI(ind) nur mit SD aus dem individuellen Pre-Intervall

\[ RCI_{ind,preSD} = \frac{\overline{x_{2}} - \overline{x_{1}}} {SE_{D,pre}} \]

\[ SE_{D,pre} = \sqrt{2 \cdot (s_{x} \cdot (1 - r_{xy})^2)} \]

\[ \text{significance cutoff} = 1.96 \cdot SE_{D,pre} = 1.96 \cdot \sqrt{2 \cdot (s_{x} \cdot (1 - r_{xy})^2)} \]

\(\overline{x_{2}}\) = mean of subject´s posttest scores, \(\overline{x_{1}}\) = mean of subject´s pretest scores, \(SE_{D,pre}\) = standard error of difference between the test scores in the individual´s pre interval \(s_{x}\) = individual standard deviation of pretest time points, \(r_{xy}\) = reliability (internal consistency Cronbach´s \(\alpha\)) of the measure, \(\text{significance cutoff}\) = (absolute) cutoff score for reliable change (95%-criterion)

EMA_30.30

EMA_30.30$SEd_pre = sqrt(2 * (EMA_30.30$ind.pretestSD * sqrt(1 - EMA_5.5_Alpha)) ^ 2)
EMA_30.30$RCI_ind_preSD = (EMA_30.30$POST_Mean - EMA_30.30$PRE_Mean) / EMA_30.30$SEd_pre
EMA_30.30$RCI_ind_preSD_Cutoff =  1.96 * EMA_30.30$SEd_pre

# Sollen SEd_pre, RCI_ind_preSD und RCI_ind_preSD_Cutoff %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_30.30 = EMA_30.30 %>% 
#  within(., {SEd_pre[SEd_pre %in% c(-Inf,Inf)] = NA
#               RCI_ind_preSD[RCI_ind_preSD %in% c(-Inf,Inf)] = NA
#               RCI_ind_preSD_Cutoff[RCI_ind_preSD_Cutoff %in% c(-Inf,Inf)] = NA})

scatter.hist(EMA_30.30$PRE_Mean, EMA_30.30$RCI_ind_preSD, xlab = "EMA_30.30$PRE_Mean", ylab = "EMA_30.30$RCI_ind_preSD", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

Durchschnittlicher RCI(ind)-Cutoff für reliable Veränderung in EMA_30.30 = 4.494.
Korrelation RCI(ind) nur mit Pre-SD (je 30 MZP) mit PHQ-Baseline (Pre-Intervall-Mean) = -0.594.

EMA_5.5_Window

EMA_5.5_Window$SEd_pre = sqrt(2 * (EMA_5.5_Window$ind.pretestSD * sqrt(1 - EMA_5.5_Alpha)) ^ 2)
EMA_5.5_Window$RCI_ind_preSD = (EMA_5.5_Window$POST_Mean - EMA_5.5_Window$PRE_Mean) / EMA_5.5_Window$SEd_pre
EMA_5.5_Window$RCI_ind_preSD_Cutoff =  1.96 * EMA_5.5_Window$SEd_pre

# Sollen SEd_pre, RCI_ind_preSD und RCI_ind_preSD_Cutoff %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_5.5_Window = EMA_5.5_Window %>% 
#  within(., {SEd_pre[SEd_pre %in% c(-Inf,Inf)] = NA
#               RCI_ind_preSD[RCI_ind_preSD %in% c(-Inf,Inf)] = NA
#               RCI_ind_preSD_Cutoff[RCI_ind_preSD_Cutoff %in% c(-Inf,Inf)] = NA})

scatter.hist(EMA_5.5_Window$PRE_Mean, EMA_5.5_Window$RCI_ind_preSD, xlab = "EMA_5.5_Window$PRE_Mean", ylab = "EMA_5.5_Window$RCI_ind_preSD", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

Durchschnittlicher RCI(ind)-Cutoff für reliable Veränderung in EMA_5.5_Window = 4.598.
Korrelation RCI(ind) nur mit Pre-SD (je 5 MZP) mit PHQ-Baseline (Pre-Intervall-Mean) = -0.578.

EMA_5.5_Days

EMA_5.5_Days$SEd_pre = sqrt(2 * (EMA_5.5_Days$ind.pretestSD * sqrt(1 - EMA_5.5_Alpha)) ^ 2)
EMA_5.5_Days$RCI_ind_preSD = (EMA_5.5_Days$POST_Mean - EMA_5.5_Days$PRE_Mean) / EMA_5.5_Days$SEd_pre
EMA_5.5_Days$RCI_ind_preSD_Cutoff =  1.96 * EMA_5.5_Days$SEd_pre

# Sollen SEd_pre, RCI_ind_preSD und RCI_ind_preSD_Cutoff %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_5.5_Days = EMA_5.5_Days %>% 
#  within(., {SEd_pre[SEd_pre %in% c(-Inf,Inf)] = NA
#               RCI_ind_preSD[RCI_ind_preSD %in% c(-Inf,Inf)] = NA
#               RCI_ind_preSD_Cutoff[RCI_ind_preSD_Cutoff %in% c(-Inf,Inf)] = NA})

scatter.hist(EMA_5.5_Days$PRE_Mean, EMA_5.5_Days$RCI_ind_preSD, xlab = "EMA_5.5_Days$PRE_Mean", ylab = "EMA_5.5_Days$RCI_ind_preSD", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

Durchschnittlicher RCI(ind)-Cutoff für reliable Veränderung in EMA_5.5_Days = 4.215.
Korrelation RCI(ind) nur mit Pre-SD (je 5 MZP) mit PHQ-Baseline (Pre-Intervall-Mean) = -0.567.

1.8.2 RCI(ind) mit pooled SD aus beiden individuellen Intervallen

\[ RCI_{ind} = \frac{\overline{x_{2}} - \overline{x_{1}}} {SE_{D}} \]

\[ SE_{D} = \sqrt{(s_{x}^2 + s_{y}^2) \cdot (1 - r_{xy})} \]

\[ \text{significance cutoff} = 1.96 \cdot SE_{D} = 1.96 \cdot \sqrt{(s_{x}^2 + s_{y}^2) \cdot (1 - r_{xy})} \]

\(\overline{x_{2}}\) = mean of subject´s posttest scores, \(\overline{x_{1}}\) = mean of subject´s pretest scores, \(SE_{D}\) = pooled standard error of difference between the test scores \(s_{x}\) = individual standard deviation of pretest time points, \(s_{y}\) = individual standard deviation of pretest time points, \(r_{xy}\) = reliability (internal consistency Cronbach´s \(\alpha\)) of the measure, \(\text{significance cutoff}\) = (absolute) cutoff score for reliable change (95%-criterion)

EMA_30.30

EMA_30.30$SEd_pooled = sqrt((EMA_30.30$ind.pretestSD ^ 2 + EMA_30.30$ind.posttestSD ^ 2) * (1 - EMA_5.5_Alpha))
EMA_30.30$RCI_ind_pooledSD = (EMA_30.30$POST_Mean - EMA_30.30$PRE_Mean) / EMA_30.30$SEd_pooled
EMA_30.30$RCI_ind_pooledSD_Cutoff =  1.96 * EMA_30.30$SEd_pooled

# Sollen SEd_pooled, RCI_ind_pooledSD und RCI_ind_pooledSD_Cutoff %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_30.30 = EMA_30.30 %>% 
#  within(., {SEd_pooled[SEd_pooled %in% c(-Inf,Inf)] = NA
#               RCI_ind_pooledSD[RCI_ind_pooledSD %in% c(-Inf,Inf)] = NA
#               RCI_ind_pooledSD_Cutoff[RCI_ind_pooledSD_Cutoff %in% c(-Inf,Inf)] = NA})

scatter.hist(EMA_30.30$PRE_Mean, EMA_30.30$RCI_ind_pooledSD, xlab = "EMA_30.30$PRE_Mean", ylab = "EMA_30.30$RCI_ind_pooledSD", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

Durchschnittlicher RCI(ind)-Cutoff für reliable Veränderung in EMA_30.30 = 5.558.
Korrelation RCI(ind) mit pooled SDs (je 30 MZP) mit PHQ-Baseline (Pre-Intervall-Mean) = -0.53.

EMA_5.5_Window

EMA_5.5_Window$SEd_pooled = sqrt((EMA_5.5_Window$ind.pretestSD ^ 2 + EMA_5.5_Window$ind.posttestSD ^ 2) * (1 - EMA_5.5_Alpha))
EMA_5.5_Window$RCI_ind_pooledSD = (EMA_5.5_Window$POST_Mean - EMA_5.5_Window$PRE_Mean) / EMA_5.5_Window$SEd_pooled
EMA_5.5_Window$RCI_ind_pooledSD_Cutoff =  1.96 * EMA_5.5_Window$SEd_pooled

# Sollen SEd_pooled, RCI_ind_pooledSD und RCI_ind_pooledSD_Cutoff %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_5.5_Window = EMA_5.5_Window %>% 
#  within(., {SEd_pooled[SEd_pooled %in% c(-Inf,Inf)] = NA
#               RCI_ind_pooledSD[RCI_ind_pooledSD %in% c(-Inf,Inf)] = NA
#               RCI_ind_pooledSD_Cutoff[RCI_ind_pooledSD_Cutoff %in% c(-Inf,Inf)] = NA})

scatter.hist(EMA_5.5_Window$PRE_Mean, EMA_5.5_Window$RCI_ind_pooledSD, xlab = "EMA_5.5_Window$PRE_Mean", ylab = "EMA_5.5_Window$RCI_ind_pooledSD", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

Durchschnittlicher RCI(ind)-Cutoff für reliable Veränderung in EMA_5.5_Window = 5.719.
Korrelation RCI(ind) mit pooled SDs (je 5 MZP) mit PHQ-Baseline (Pre-Intervall-Mean) = -0.515.

EMA_5.5_Days

EMA_5.5_Days$SEd_pooled = sqrt((EMA_5.5_Days$ind.pretestSD ^ 2 + EMA_5.5_Days$ind.posttestSD ^ 2) * (1 - EMA_5.5_Alpha))
EMA_5.5_Days$RCI_ind_pooledSD = (EMA_5.5_Days$POST_Mean - EMA_5.5_Days$PRE_Mean) / EMA_5.5_Days$SEd_pooled
EMA_5.5_Days$RCI_ind_pooledSD_Cutoff =  1.96 * EMA_5.5_Days$SEd_pooled

# Sollen SEd_pooled, RCI_ind_pooledSD und RCI_ind_pooledSD_Cutoff %in% c(-Inf,Inf) ein-/ausgeschlossen werden?
#EMA_5.5_Days = EMA_5.5_Days %>% 
#  within(., {SEd_pooled[SEd_pooled %in% c(-Inf,Inf)] = NA
#               RCI_ind_pooledSD[RCI_ind_pooledSD %in% c(-Inf,Inf)] = NA
#               RCI_ind_pooledSD_Cutoff[RCI_ind_pooledSD_Cutoff %in% c(-Inf,Inf)] = NA})

scatter.hist(EMA_5.5_Days$PRE_Mean, EMA_5.5_Days$RCI_ind_pooledSD, xlab = "EMA_5.5_Days$PRE_Mean", ylab = "EMA_5.5_Days$RCI_ind_pooledSD", ellipse = FALSE, grid = TRUE, col = c("dodgerblue", "darkorange"))

Durchschnittlicher RCI(ind)-Cutoff für reliable Veränderung in EMA_5.5_Days = 5.394.
Korrelation RCI(ind) mit pooled SDs (je 5 MZP) mit PHQ-Baseline (Pre-Intervall-Mean) = -0.548.

1.9 Vergleich RCI(ind) (nur Pre-SD) - RCI(ind) (pooled SDs)

scatter.hist(EMA_30.30$RCI_ind_preSD, EMA_30.30$RCI_ind_pooledSD, xlab = "EMA_30.30$RCI_ind_preSD", ylab =
               "EMA_30.30$RCI_ind_pooledSD", ellipse = FALSE, grid = TRUE, col = c("dodgerblue",  "darkorange"))

scatter.hist(EMA_5.5_Window$RCI_ind_preSD, EMA_5.5_Window$RCI_ind_pooledSD, xlab = "EMA_5.5_Window$RCI_ind_preSD", ylab =
               "EMA_5.5_Window$RCI_ind_pooledSD", ellipse = FALSE, grid = TRUE, col = c("dodgerblue",  "darkorange"))

scatter.hist(EMA_5.5_Days$RCI_ind_preSD, EMA_5.5_Days$RCI_ind_pooledSD, xlab = "EMA_5.5_Days$RCI_ind_preSD", ylab =
               "EMA_5.5_Days$RCI_ind_pooledSD", ellipse = FALSE, grid = TRUE, col = c("dodgerblue",  "darkorange"))

1.10 RCI-Klassifikationen

RCI_Int = tibble(RCI = c("RCI < -1,96","-1,96 <= RCI <= 1,96","RCI > 1,96"),
                Klassifikation = c(-1,0,1),
                Interpretation = c("reliable Verbesserung","keine reliable Veränderung","reliable Verschlechterung"))

EMA_30.30: RCI(ind) nur mit Pre-SDs

EMA_30.30 = EMA_30.30 %>% 
  mutate(RCI_ind_preSD_klass = case_when(
    RCI_ind_preSD < -1.96 ~ -1,
    RCI_ind_preSD >= -1.96 & RCI_ind_preSD < 1.96 ~ 0,
    RCI_ind_preSD > 1.96 ~ 1,
    TRUE ~ RCI_ind_preSD
  )
)

temp = EMA_30.30 %>% 
  count(RCI_ind_preSD_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

RCI_Int %>%
  dplyr::rename(RCI_ind_preSD_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

RCI	RCI_ind_preSD_klass	Interpretation	n	Percentage
RCI < -1,96	-1	reliable Verbesserung	37	37
-1,96 <= RCI <= 1,96	0	keine reliable Veränderung	63	63
RCI > 1,96	1	reliable Verschlechterung	NA	NA

EMA_30.30: RCI(ind) mit pooled SDs

EMA_30.30 = EMA_30.30 %>% 
  mutate(RCI_ind_pooledSD_klass = case_when(
    RCI_ind_pooledSD < -1.96 ~ -1,
    RCI_ind_pooledSD >= -1.96 & RCI_ind_pooledSD < 1.96 ~ 0,
    RCI_ind_pooledSD > 1.96 ~ 1,
    TRUE ~ RCI_ind_pooledSD
  )
)

temp = EMA_30.30 %>% 
  count(RCI_ind_pooledSD_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

RCI_Int %>%
  dplyr::rename(RCI_ind_pooledSD_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

RCI	RCI_ind_pooledSD_klass	Interpretation	n	Percentage
RCI < -1,96	-1	reliable Verbesserung	28	28
-1,96 <= RCI <= 1,96	0	keine reliable Veränderung	72	72
RCI > 1,96	1	reliable Verschlechterung	NA	NA

EMA_5.5_Window: RCI(ind) nur mit Pre-SDs

EMA_5.5_Window = EMA_5.5_Window %>% 
  mutate(RCI_ind_preSD_klass = case_when(
    RCI_ind_preSD < -1.96 ~ -1,
    RCI_ind_preSD >= -1.96 & RCI_ind_preSD < 1.96 ~ 0,
    RCI_ind_preSD > 1.96 ~ 1,
    TRUE ~ RCI_ind_preSD
  )
)

temp = EMA_5.5_Window %>% 
  count(RCI_ind_preSD_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

RCI_Int %>%
  dplyr::rename(RCI_ind_preSD_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

RCI	RCI_ind_preSD_klass	Interpretation	n	Percentage
RCI < -1,96	-1	reliable Verbesserung	39	39
-1,96 <= RCI <= 1,96	0	keine reliable Veränderung	59	59
RCI > 1,96	1	reliable Verschlechterung	2	2

EMA_5.5_Window: RCI(ind) mit pooled SDs

EMA_5.5_Window = EMA_5.5_Window %>% 
  mutate(RCI_ind_pooledSD_klass = case_when(
    RCI_ind_pooledSD < -1.96 ~ -1,
    RCI_ind_pooledSD >= -1.96 & RCI_ind_pooledSD < 1.96 ~ 0,
    RCI_ind_pooledSD > 1.96 ~ 1,
    TRUE ~ RCI_ind_pooledSD
  )
)

temp = EMA_5.5_Window %>% 
  count(RCI_ind_pooledSD_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

RCI_Int %>%
  dplyr::rename(RCI_ind_pooledSD_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

RCI	RCI_ind_pooledSD_klass	Interpretation	n	Percentage
RCI < -1,96	-1	reliable Verbesserung	28	28
-1,96 <= RCI <= 1,96	0	keine reliable Veränderung	71	71
RCI > 1,96	1	reliable Verschlechterung	1	1

EMA_5.5_Days: RCI(ind) nur mit Pre-SDs

EMA_5.5_Days = EMA_5.5_Days %>% 
  mutate(RCI_ind_preSD_klass = case_when(
    RCI_ind_preSD < -1.96 ~ -1,
    RCI_ind_preSD >= -1.96 & RCI_ind_preSD < 1.96 ~ 0,
    RCI_ind_preSD > 1.96 ~ 1,
    TRUE ~ RCI_ind_preSD
  )
)

temp = EMA_5.5_Days %>% 
  count(RCI_ind_preSD_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

RCI_Int %>%
  dplyr::rename(RCI_ind_preSD_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

RCI	RCI_ind_preSD_klass	Interpretation	n	Percentage
RCI < -1,96	-1	reliable Verbesserung	45	45
-1,96 <= RCI <= 1,96	0	keine reliable Veränderung	53	53
RCI > 1,96	1	reliable Verschlechterung	2	2

EMA_5.5_Days: RCI(ind) mit pooled SDs

EMA_5.5_Days = EMA_5.5_Days %>% 
  mutate(RCI_ind_pooledSD_klass = case_when(
    RCI_ind_pooledSD < -1.96 ~ -1,
    RCI_ind_pooledSD >= -1.96 & RCI_ind_pooledSD < 1.96 ~ 0,
    RCI_ind_pooledSD > 1.96 ~ 1,
    TRUE ~ RCI_ind_pooledSD
  )
)

temp = EMA_5.5_Days %>% 
  count(RCI_ind_pooledSD_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

RCI_Int %>%
  dplyr::rename(RCI_ind_pooledSD_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

RCI	RCI_ind_pooledSD_klass	Interpretation	n	Percentage
RCI < -1,96	-1	reliable Verbesserung	33	33
-1,96 <= RCI <= 1,96	0	keine reliable Veränderung	65	65
RCI > 1,96	1	reliable Verschlechterung	2	2

1.11 Edwards-Nunnally-Methode (EN) nach Speer (1992)

\[ \bigl[ r_{xx} (X_{pre} - M_{pre}) + M_{pre} \bigr] \pm 2 \cdot S_{pre} \cdot \sqrt{1 - r_{xx}} \]

\(r_{xx}\) = reliability of the measure, \(X_{pre}\) = individual´s raw score at pre-treatment, \(M_{pre}\) = mean of the sample at pre-treatment, \(S_{pre}\) = standard deviation of the sample at pre-treatment

Interpretation der Post-Ausprägung nach EN-Intervall-Methode

EN_Int = tibble(EN = c("PHQ POST < [EN-Intervall]","PHQ POST im [EN-Intervall]","PHQ POST > [EN-Intervall]"),
                Klassifikation = c(-1,0,1), Interpretation = c("signifikante Verbesserung",
                        "keine signifikante Veränderung","signifikante Verschlechterung"))

EN-Intervalle in EMA_30.30

EMA_30.30$EN_min = (EMA_5.5_Alpha * (EMA_30.30$PRE_Mean - mean(EMA_30.30$PRE_Mean)) + mean(EMA_30.30$PRE_Mean)) - 2 * mean(EMA_30.30$ind.pretestSD) * sqrt(1 - EMA_5.5_Alpha)

EMA_30.30$EN_max = (EMA_5.5_Alpha * (EMA_30.30$PRE_Mean - mean(EMA_30.30$PRE_Mean)) + mean(EMA_30.30$PRE_Mean)) + 2 * mean(EMA_30.30$ind.pretestSD) * sqrt(1 - EMA_5.5_Alpha)

EMA_30.30 = EMA_30.30 %>% 
  mutate(EN_klass = case_when(
    POST_Mean > EN_max ~ 1,
    POST_Mean < EN_max & POST_Mean > EN_min ~ 0,
    POST_Mean < EN_min ~ -1,
    TRUE ~ POST_Mean
  )
)

temp = EMA_30.30 %>% 
  count(EN_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

EN_Int %>%
  dplyr::rename(EN_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

EN	EN_klass	Interpretation	n	Percentage
PHQ POST < [EN-Intervall]	-1	signifikante Verbesserung	46	46
PHQ POST im [EN-Intervall]	0	keine signifikante Veränderung	54	54
PHQ POST > [EN-Intervall]	1	signifikante Verschlechterung	NA	NA

EN-Intervalle in EMA_5.5_Window

EMA_5.5_Window$EN_min = (EMA_5.5_Alpha * (EMA_5.5_Window$PRE_Mean - mean(EMA_5.5_Window$PRE_Mean)) + 
                           mean(EMA_5.5_Window$PRE_Mean)) - 2 *  mean(EMA_5.5_Window$ind.pretestSD) * sqrt(1 - EMA_5.5_Alpha)

EMA_5.5_Window$EN_max = (EMA_5.5_Alpha * (EMA_5.5_Window$PRE_Mean - mean(EMA_5.5_Window$PRE_Mean)) + 
                           mean(EMA_5.5_Window$PRE_Mean)) + 2 * mean(EMA_5.5_Window$ind.pretestSD) * sqrt(1 - EMA_5.5_Alpha)

EMA_5.5_Window = EMA_5.5_Window %>% 
  mutate(EN_klass = case_when(
    POST_Mean > EN_max ~ 1,
    POST_Mean < EN_max & POST_Mean > EN_min ~ 0,
    POST_Mean < EN_min ~ -1,
    TRUE ~ POST_Mean
  )
)

temp = EMA_5.5_Window %>% 
  count(EN_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

EN_Int %>%
  dplyr::rename(EN_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

EN	EN_klass	Interpretation	n	Percentage
PHQ POST < [EN-Intervall]	-1	signifikante Verbesserung	46	46
PHQ POST im [EN-Intervall]	0	keine signifikante Veränderung	53	53
PHQ POST > [EN-Intervall]	1	signifikante Verschlechterung	1	1

EN-Intervalle in EMA_5.5_Days

EMA_5.5_Days$EN_min = (EMA_5.5_Alpha * (EMA_5.5_Days$PRE_Mean - mean(EMA_5.5_Days$PRE_Mean)) + 
                           mean(EMA_5.5_Days$PRE_Mean)) - 2 *  mean(EMA_5.5_Days$ind.pretestSD) * sqrt(1 - EMA_5.5_Alpha)

EMA_5.5_Days$EN_max = (EMA_5.5_Alpha * (EMA_5.5_Days$PRE_Mean - mean(EMA_5.5_Days$PRE_Mean)) + 
                           mean(EMA_5.5_Days$PRE_Mean)) + 2 * mean(EMA_5.5_Days$ind.pretestSD) * sqrt(1 - EMA_5.5_Alpha)

EMA_5.5_Days = EMA_5.5_Days %>% 
  mutate(EN_klass = case_when(
    POST_Mean > EN_max ~ 1,
    POST_Mean < EN_max & POST_Mean > EN_min ~ 0,
    POST_Mean < EN_min ~ -1,
    TRUE ~ POST_Mean
  )
)

temp = EMA_5.5_Days %>% 
  count(EN_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

EN_Int %>%
  dplyr::rename(EN_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

EN	EN_klass	Interpretation	n	Percentage
PHQ POST < [EN-Intervall]	-1	signifikante Verbesserung	54	54
PHQ POST im [EN-Intervall]	0	keine signifikante Veränderung	44	44
PHQ POST > [EN-Intervall]	1	signifikante Verschlechterung	2	2

1.12 Clinically Significant Improvement (CSI)

Clinically Significant Improvement (CSI) vom Pre- zum Post-Intervall

“The original validation study of the PHQ-9 defined clinically significant improvement as [a pre-treatment score >= 10 and] a post-treatment score of <= 9 combined with improvement of 50%.” (McMillan, Gilbody, & Richards, 2010)

CSI_Int = tibble(CSI = c("Pre-Score >= 10 & Post-Score <= 9 & PC >= 50", "every other combination", 
                         "Pre-Score <= 9 & Post-Score >= 10 & PC <= -50"),
                Klassifikation = c(-1,0,1),
                Interpretation = c("klinisch signifikante Verbesserung", "keine klinisch signifikante Veränderung", 
                                   "klinisch signifikante Verschlechterung"))

1.12.1 CSI in EMA_30.30

EMA_30.30 = EMA_30.30 %>% 
   mutate(CSI_klass = case_when(
     PRE_Mean >= 10 & POST_Mean <= 9 & Mean_PC >= 50 ~ -1,
     PRE_Mean <= 9 & POST_Mean >= 10 & Mean_PC <= -50 ~ 1,
     TRUE ~ 0
   )
)

temp = EMA_30.30 %>% 
  count(CSI_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

CSI_Int %>%
  dplyr::rename(CSI_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

CSI	CSI_klass	Interpretation	n	Percentage
Pre-Score >= 10 & Post-Score <= 9 & PC >= 50	-1	klinisch signifikante Verbesserung	19	19
every other combination	0	keine klinisch signifikante Veränderung	81	81
Pre-Score <= 9 & Post-Score >= 10 & PC <= -50	1	klinisch signifikante Verschlechterung	NA	NA

1.12.2 CSI in EMA_5.5_Window

EMA_5.5_Window = EMA_5.5_Window %>% 
   mutate(CSI_klass = case_when(
     PRE_Mean >= 10 & POST_Mean <= 9 & Mean_PC >= 50 ~ -1,
     PRE_Mean <= 9 & POST_Mean >= 10 & Mean_PC <= -50 ~ 1,
     TRUE ~ 0
   )
)

temp = EMA_5.5_Window %>% 
  count(CSI_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

CSI_Int %>%
  dplyr::rename(CSI_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

CSI	CSI_klass	Interpretation	n	Percentage
Pre-Score >= 10 & Post-Score <= 9 & PC >= 50	-1	klinisch signifikante Verbesserung	24	24
every other combination	0	keine klinisch signifikante Veränderung	75	75
Pre-Score <= 9 & Post-Score >= 10 & PC <= -50	1	klinisch signifikante Verschlechterung	1	1

1.12.3 CSI in EMA_5.5_Days

EMA_5.5_Days = EMA_5.5_Days %>% 
   mutate(CSI_klass = case_when(
     PRE_Mean >= 10 & POST_Mean <= 9 & Mean_PC >= 50 ~ -1,
     PRE_Mean <= 9 & POST_Mean >= 10 & Mean_PC <= -50 ~ 1,
     TRUE ~ 0
   )
)

temp = EMA_5.5_Days %>% 
  count(CSI_klass) %>% 
  mutate(Percentage = round(((n / sum(n)) * 100), digits = 2))

CSI_Int %>%
  dplyr::rename(CSI_klass = Klassifikation) %>%
  full_join(., temp) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

CSI	CSI_klass	Interpretation	n	Percentage
Pre-Score >= 10 & Post-Score <= 9 & PC >= 50	-1	klinisch signifikante Verbesserung	23	23
every other combination	0	keine klinisch signifikante Veränderung	75	75
Pre-Score <= 9 & Post-Score >= 10 & PC <= -50	1	klinisch signifikante Verschlechterung	2	2

1.13 Sudden Gains

Sudden Gain/Loss-Klassifikation vom Pre- zum Post-Intervall mithilfe des R-Packages “suddengains”

3 Kriterien nach Tang & DeRubeis (1999): bedeutende absolute Veränderung: Über-/Unterschreitung eines definierten Cutoff-Scores (z.B. RCI), hier PHQ-9-Score <= 9 bedeutende relative Veränderung: Reduktion/Zuwachs von Pre zu Post um >= 25% bedeutende Veränderung relativ zur Symptom-Fluktuation:

\[ M_{pre} - M_{post} > \text{critical value} \cdot \sqrt{\frac{\left(n_{pre} - 1 \right) \cdot SD^2_{pre} + \left(n_{post} - 1 \right) \cdot SD^2_{post}} {n_{pre} + n_{post} - 2}} \]

\(M_{pre}\) = mean of the subject´s scores before a potential gain/loss, \(M_{post}\) = mean of the subject´s scores after a potential gain/loss, \(\text{critical value}\) = 2.776 = two-tailed t statistic for \(\alpha\) = 0.05 and df = 4, \(n_{pre}\) = number of measurement points before a potential gain/loss, \(n_{post}\) = number of measurement points after a potential gain/loss, \(SD^2_{pre}\) = standard deviation of the subject´s scores before a potential gain/loss, \(SD^2_{post}\) = standard deviation of the subject´s scores after a potential gain/loss

SG_Int = tibble(SG = c("PHQ-9 Post-Mean <= 9 & (Mean) PC >= 25 & Mean Diff. > (absolute) critical fluctuation", 
                       "every other combination of conditions", 
                       "PHQ-9 Post-Mean > 9 & (Mean) PC <= -25 & Mean Diff. > (absolute) critical fluctuation"),
                Klassifikation = c(-1,0,1),
                Interpretation = c("sudden gain", "no sudden change", "sudden loss"))

1.13.1 Sudden Gains/Losses in EMA_30.30

1.13.2 Sudden Gains/Losses in EMA_5.5_Window

1.13.3 Sudden Gains/Losses in EMA_5.5_Days

1.14 Individuelle Übereinstimmung der Klassifikationen

Übereinstimmung der Klassifikationen auf individueller Ebene zwischen EMA_30.30, EMA_5.5_Window und EMA_5.5_Days

Interpretation von Cohen´s Kappa:

tibble(Cohen_Kappa = c("k < .20",".21 <= k < .40",".41 <= k < .60",".61 <= k < .80","k > .80"),
       Interpretation = c("poor","fair","moderate","good","very good")) %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

Cohen_Kappa	Interpretation
k < .20	poor
.21 <= k < .40	fair
.41 <= k < .60	moderate
.61 <= k < .80	good
k > .80	very good

1.14.1 Klinische PHQ-9-Interpretation

Übereinstimmung zwischen den klinischen Interpretationen der PHQ-9-Werte für Pre- und Post-Intervalle (je 30 MZP und je 5 MZP):

# PRE
x = EMA_30.30 %>% 
  select(ID, PRE_Mean_klass) %>% 
  dplyr::rename(PRE_klass_30.30 = PRE_Mean_klass)

y = EMA_5.5_Window %>% 
  select(ID, PRE_Mean_klass) %>% 
  dplyr::rename(PRE_klass_5.5_Window = PRE_Mean_klass)

z = EMA_5.5_Days %>% 
  select(ID, PRE_Mean_klass) %>% 
  dplyr::rename(PRE_klass_5.5_Days = PRE_Mean_klass)

temp = full_join(x, y, by = "ID") %>% 
  full_join(., z, by = "ID") %>% 
  select(-ID) %>% 
  mutate(across(.cols = everything(), as.factor))

### Cohen´s Kappa
rnames = c("PRE_klass_30.30", "PRE_klass_5.5_Window", "PRE_klass_5.5_Days")

Agreement = matrix(ncol = 3, nrow = 3, dimnames = list(rnames, rnames))

for (i in 1:nrow(Agreement)) {
  for (j in 1:ncol(Agreement)) {
    x = eval(parse(text = paste0("temp$", names(temp[,i]))))
    y = eval(parse(text = paste0("temp$", names(temp[,j]))))
    
    Agreement[i,j] = CohenKappa(x = x, y = y)
  }
}

# mit plot.matrix::...
par(mar = c(5.1, 4.1, 4.1, 4.1)) # default c(5.1, 4.1, 4.1, 2.1)
plot(Agreement, col = heat.colors(n=5, rev=TRUE), fmt.cell = "%.2f", cex.axis = 0.7, cex = 0.8, las = 2, 
     key = list(cex.axis=0.7), ann = FALSE, breaks = c(0, 0.21, 0.41, 0.61, 0.81, 1));
  title(main = "Übereinstimmung (Cohen´s Kappa) der PHQ-PRE-Klassifikationen")

# POST
x = EMA_30.30 %>% 
  select(ID, POST_Mean_klass) %>% 
  dplyr::rename(POST_klass_30.30 = POST_Mean_klass)

y = EMA_5.5_Window %>% 
  select(ID, POST_Mean_klass) %>% 
  dplyr::rename(POST_klass_5.5_Window = POST_Mean_klass)

z = EMA_5.5_Days %>% 
  select(ID, POST_Mean_klass) %>% 
  dplyr::rename(POST_klass_5.5_Days = POST_Mean_klass)

temp = full_join(x, y, by = "ID") %>% 
  full_join(., z, by = "ID") %>% 
  select(-ID) %>% 
  mutate(across(.cols = everything(), as.factor))

### Cohen´s Kappa
rnames = c("POST_klass_30.30", "POST_klass_5.5_Window", "POST_klass_5.5_Days")

Agreement = matrix(ncol = 3, nrow = 3, dimnames = list(rnames, rnames))

for (i in 1:nrow(Agreement)) {
  for (j in 1:ncol(Agreement)) {
    x = eval(parse(text = paste0("temp$", names(temp[,i]))))
    y = eval(parse(text = paste0("temp$", names(temp[,j]))))
    
    Agreement[i,j] = CohenKappa(x = x, y = y)
  }
}

# mit plot.matrix::...
par(mar = c(5.1, 4.1, 4.1, 4.1)) # default c(5.1, 4.1, 4.1, 2.1)
plot(Agreement, col = heat.colors(n=5, rev=TRUE), fmt.cell = "%.2f", cex.axis = 0.7, cex = 0.8, las = 2, 
     key = list(cex.axis=0.7), ann = FALSE, breaks = c(0, 0.21, 0.41, 0.61, 0.81, 1));
  title(main = "Übereinstimmung (Cohen´s Kappa) der PHQ-POST-Klassifikationen")

1.14.2 Zusammenfassung der Klassifikations-Häufigkeiten

# einheitliche Kodierung von Verbesserung (-1), keiner Veränderung (0) und Verschlechterung (1):

x = EMA_30.30 %>% 
  select(ID, Mean_PC_klass, RCI_ind_preSD_klass, RCI_ind_pooledSD_klass, EN_klass, CSI_klass) %>% 
  dplyr::rename(Mean_PC_30.30 = Mean_PC_klass, RCI_ind_preSD_30.30 = RCI_ind_preSD_klass, 
         RCI_ind_pooledSD_30.30 = RCI_ind_pooledSD_klass, EN_30.30 = EN_klass, CSI_30.30 = CSI_klass) %>% 
  mutate(Mean_PC_30.30 = recode(Mean_PC_30.30, '-2' = 1L, '-1' = 0L, '0' = 0L, '1' = 0L, '2' = -1L))

y = EMA_5.5_Window %>% 
  select(ID, Mean_PC_klass, RCI_ind_preSD_klass, RCI_ind_pooledSD_klass, EN_klass, CSI_klass) %>% 
  dplyr::rename(Mean_PC_5.5_Window = Mean_PC_klass, RCI_ind_preSD_5.5_Window = RCI_ind_preSD_klass, 
         RCI_ind_pooledSD_5.5_Window = RCI_ind_pooledSD_klass, EN_5.5_Window = EN_klass, CSI_5.5_Window = CSI_klass) %>% 
  mutate(Mean_PC_5.5_Window = recode(Mean_PC_5.5_Window, '-2' = 1L, '-1' = 0L, '0' = 0L, '1' = 0L, '2' = -1L))

z = EMA_5.5_Days %>% 
  select(ID, Mean_PC_klass, RCI_ind_preSD_klass, RCI_ind_pooledSD_klass, EN_klass, CSI_klass) %>% 
  dplyr::rename(Mean_PC_5.5_Days = Mean_PC_klass, RCI_ind_preSD_5.5_Days = RCI_ind_preSD_klass, 
         RCI_ind_pooledSD_5.5_Days = RCI_ind_pooledSD_klass, EN_5.5_Days = EN_klass, CSI_5.5_Days = CSI_klass) %>% 
  mutate(Mean_PC_5.5_Days = recode(Mean_PC_5.5_Days, '-2' = 1L, '-1' = 0L, '0' = 0L, '1' = 0L, '2' = -1L))

temp = full_join(x, y, by = "ID") %>% 
  full_join(., z, "ID") %>% 
  select(-ID) %>% 
  dplyr::mutate(across(.cols = everything(), as.factor))

rnames = names(temp)


#view(dfSummary(temp))
#dfSummary(temp, plain.ascii = FALSE, style = 'grid', graph.magnif = 0.75, valid.col = FALSE, tmp.img.dir = "/tmp")
#dfSummary(temp)
print(dfSummary(temp, varnumbers = FALSE, plain.ascii = FALSE, style = 'grid', graph.magnif = 0.75, valid.col = FALSE, na.col = FALSE, display.labels = FALSE, silent = FALSE, headers = FALSE, footnote = NA, tmp.img.dir = "/tmp"), method = 'render')

Data Frame Summary

temp

Dimensions: 100 x 15
Duplicates: 49

Variable

Stats / Values

Freqs (% of Valid)

Graph

Mean_PC_30.30 [factor]

1. -1 2. 0

23	(	23.0%	)
77	(	77.0%	)

RCI_ind_preSD_30.30 [factor]

1. -1 2. 0

37	(	37.0%	)
63	(	63.0%	)

RCI_ind_pooledSD_30.30 [factor]

1. -1 2. 0

28	(	28.0%	)
72	(	72.0%	)

EN_30.30 [factor]

1. -1 2. 0

46	(	46.0%	)
54	(	54.0%	)

CSI_30.30 [factor]

1. -1 2. 0

19	(	19.0%	)
81	(	81.0%	)

Mean_PC_5.5_Window [factor]

1. -1 2. 0 3. 1

26	(	26.0%	)
72	(	72.0%	)
2	(	2.0%	)

RCI_ind_preSD_5.5_Window [factor]

1. -1 2. 0 3. 1

39	(	39.0%	)
59	(	59.0%	)
2	(	2.0%	)

RCI_ind_pooledSD_5.5_Window [factor]

1. -1 2. 0 3. 1

28	(	28.0%	)
71	(	71.0%	)
1	(	1.0%	)

EN_5.5_Window [factor]

1. -1 2. 0 3. 1

46	(	46.0%	)
53	(	53.0%	)
1	(	1.0%	)

CSI_5.5_Window [factor]

1. -1 2. 0 3. 1

24	(	24.0%	)
75	(	75.0%	)
1	(	1.0%	)

Mean_PC_5.5_Days [factor]

1. -1 2. 0 3. 1

29	(	29.0%	)
69	(	69.0%	)
2	(	2.0%	)

RCI_ind_preSD_5.5_Days [factor]

1. -1 2. 0 3. 1

45	(	45.0%	)
53	(	53.0%	)
2	(	2.0%	)

RCI_ind_pooledSD_5.5_Days [factor]

1. -1 2. 0 3. 1

33	(	33.0%	)
65	(	65.0%	)
2	(	2.0%	)

EN_5.5_Days [factor]

1. -1 2. 0 3. 1

54	(	54.0%	)
44	(	44.0%	)
2	(	2.0%	)

CSI_5.5_Days [factor]

1. -1 2. 0 3. 1

23	(	23.0%	)
75	(	75.0%	)
2	(	2.0%	)

Generated by summarytools 0.9.6 (R version 4.0.2)
2020-10-30

1.14.3 Übereinstimmung der Klassifikations-Häufigkeiten

Gesamt-Übereinstimmung

### Cohen´s Kappa
Agreement = matrix(ncol = 15, nrow = 15, dimnames = list(rnames, rnames))

for (i in 1:nrow(Agreement)) {
  for (j in 1:ncol(Agreement)) {
    x = eval(parse(text = paste0("temp$", names(temp[,i]))))
    y = eval(parse(text = paste0("temp$", names(temp[,j]))))
    
    Agreement[i,j] = CohenKappa(x = x, y = y)
  }
}

# mit plot.matrix::...
par(mar = c(5.1, 4.1, 4.1, 4.1)) # default c(5.1, 4.1, 4.1, 2.1)
plot(Agreement, col = heat.colors(n=5, rev=TRUE), fmt.cell = "%.2f", cex.axis = 0.5, cex = 0.7, las = 2, 
     key = list(cex.axis=0.6), ann = FALSE, breaks = c(0, 0.21, 0.41, 0.61, 0.81, 1));
  title(main = "Übereinstimmung (Cohen´s Kappa) der Klassifikationen")

### Prozentuale Übereinstimmung
Percentage_Agreement = matrix(ncol = 15, nrow = 15, dimnames = list(rnames, rnames))

for (i in 1:nrow(Percentage_Agreement)) {
  for (j in 1:ncol(Percentage_Agreement)) {
    x = eval(parse(text = paste0("temp$", names(temp[,i]))))
    y = eval(parse(text = paste0("temp$", names(temp[,j]))))
    
    Percentage_Agreement[i,j] = Agree(cbind(x, y))[1]
  }
}

# mit plot.matrix::...
par(mar = c(5.1, 4.1, 4.1, 4.1)) # default c(5.1, 4.1, 4.1, 2.1)
plot(Percentage_Agreement, col = heat.colors(n=4, rev=TRUE), fmt.cell = "%.2f", cex.axis = 0.5, cex = 0.7, las = 2, 
     key = list(cex.axis=0.6), ann = FALSE, breaks = c(0, 0.26, 0.51, 0.76, 1));
  title(main = "Prozentuale Übereinstimmung der Klassifikationen")

Übereinstimmung nur für Verbesserung (-1)

### Cohen´s Kappa
Agreement = matrix(ncol = 15, nrow = 15, dimnames = list(rnames, rnames))

for (i in 1:nrow(Agreement)) {
  for (j in 1:ncol(Agreement)) {
    x = eval(parse(text = paste0("temp$", names(temp[,i])))) %>% 
      dplyr::recode_factor(., '-1' = -1L)
    y = eval(parse(text = paste0("temp$", names(temp[,j])))) %>% 
      dplyr::recode_factor(., '-1' = -1L)
    
    Agreement[i,j] = CohenKappa(x = x, y = y, useNA = "ifany")
  }
}

# mit plot.matrix::...
par(mar = c(5.1, 4.1, 4.1, 4.1)) # default c(5.1, 4.1, 4.1, 2.1)
plot(Agreement, col = heat.colors(n=5, rev=TRUE), fmt.cell = "%.2f", cex.axis = 0.5, cex = 0.7, las = 2, 
     key = list(cex.axis=0.6), ann = FALSE, breaks = c(0, 0.21, 0.41, 0.61, 0.81, 1));
  title(main = "Übereinstimmung (Cohen´s Kappa): Verbesserung (-1)")

### Prozentuale Übereinstimmung
Percentage_Agreement = matrix(ncol = 15, nrow = 15, dimnames = list(rnames, rnames))

for (i in 1:nrow(Percentage_Agreement)) {
  for (j in 1:ncol(Percentage_Agreement)) {
    x = eval(parse(text = paste0("temp$", names(temp[,i]))))
    y = eval(parse(text = paste0("temp$", names(temp[,j]))))
    
    Percentage_Agreement[i,j] = length(which(x == -1L & y == -1L)) / 
      length(which(x == -1L | y == -1L))
  }
}

# mit plot.matrix::...
par(mar = c(5.1, 4.1, 4.1, 4.1)) # default c(5.1, 4.1, 4.1, 2.1)
plot(Percentage_Agreement, col = heat.colors(n=4, rev=TRUE), fmt.cell = "%.2f", cex.axis = 0.5, cex = 0.7, las = 2, 
     key = list(cex.axis=0.6), ann = FALSE, breaks = c(0, 0.26, 0.51, 0.76, 1));
  title(main = "Prozentuale Übereinstimmung: Verbesserung (-1)")

Übereinstimmung nur für Verschlechterung (1)

### Cohen´s Kappa
Agreement = matrix(ncol = 15, nrow = 15, dimnames = list(rnames, rnames))

for (i in 1:nrow(Agreement)) {
  for (j in 1:ncol(Agreement)) {
    x = eval(parse(text = paste0("temp$", names(temp[,i])))) %>% 
      recode_factor(., '1' = 1L)
    y = eval(parse(text = paste0("temp$", names(temp[,j])))) %>% 
      recode_factor(., '1' = 1L)
    
    Agreement[i,j] = CohenKappa(x = x, y = y, useNA = "ifany")
  }
}

# mit plot.matrix::...
par(mar = c(5.1, 4.1, 4.1, 4.1)) # default c(5.1, 4.1, 4.1, 2.1)
plot(Agreement, col = heat.colors(n=5, rev=TRUE), fmt.cell = "%.2f", cex.axis = 0.5, cex = 0.7, las = 2, 
     key = list(cex.axis=0.6), ann = FALSE, breaks = c(0, 0.21, 0.41, 0.61, 0.81, 1));
  title(main = "Übereinstimmung (Cohen´s Kappa): Verschlechterung (1)")

### Prozentuale Übereinstimmung
Percentage_Agreement = matrix(ncol = 15, nrow = 15, dimnames = list(rnames, rnames))

for (i in 1:nrow(Percentage_Agreement)) {
  for (j in 1:ncol(Percentage_Agreement)) {
    x = eval(parse(text = paste0("temp$", names(temp[,i]))))
    y = eval(parse(text = paste0("temp$", names(temp[,j]))))
    
    Percentage_Agreement[i,j] = length(which(x == 1L & y == 1L)) / 
      length(which(x == 1L | y == 1L))
  }
}

# mit plot.matrix::...
par(mar = c(5.1, 4.1, 4.1, 4.1)) # default c(5.1, 4.1, 4.1, 2.1)
plot(Percentage_Agreement, col = heat.colors(n=4, rev=TRUE), fmt.cell = "%.2f", cex.axis = 0.5, cex = 0.7, las = 2, 
     key = list(cex.axis=0.6), ann = FALSE, breaks = c(0, 0.26, 0.51, 0.76, 1));
  title(main = "Prozentuale Übereinstimmung: Verschlechterung (1)")

1.15 Sensitivität und Spezifität der Klassifikationsmethoden

Diagnostische Sensitivität und Spezifität einer “neuen” Testmethode im Vergleich zu einer “Goldstandard”-Testmethode:
Sensitivität = Wahrscheinlichkeit für ein richtig-positives Testergebnis
Spezifität = Wahrscheinlichkeit für ein richtig-negatives Testergebnis

\[ Sensitivity = \frac{\sum{\text{True Positives}}} {\sum{\text{True Positives}} + \sum{\text{False Negatives}}} \]

\[ Specificity = \frac{\sum{\text{True Negatives}}} {\sum{\text{True Negatives}} + \sum{\text{False Positives}}} \]

Sensitivität & Spezifität gegenüber Veränderung:
Absolute Häufigkeiten der Veränderungs-Klassifikationen (verändert vs. nicht verändert) der Klassifikationsmethoden im Vergleich zur klinischen Signifikanz CSI (je 30 MZP) als “Goldstandard”:

SenSpez = tibble(Method = colnames(temp),
                 n_Changed = as.integer(NA),
                 n_Unchanged = as.integer(NA),
                 Total = as.integer(NA),
                 Sensitivity = as.numeric(NA),
                 Specificity = as.numeric(NA))

for (i in 1:nrow(SenSpez)) {
  x = eval(parse(text = paste0("temp$", names(temp[,i]))))
  SenSpez[i,"n_Changed"] = temp %>% summarise(., sum(x %in% c(-1,1))) %>% as.integer()
}

for (i in 1:nrow(SenSpez)) {
  x = eval(parse(text = paste0("temp$", names(temp[,i]))))
  SenSpez[i,"n_Unchanged"] = temp %>% summarise(., sum(x == 0)) %>% as.integer()
}

for (i in 1:nrow(SenSpez)) {
  x = eval(parse(text = paste0("temp$", names(temp[,i]))))
  SenSpez[i,"Total"] = temp %>% summarise(., sum(!is.na(x))) %>% as.integer()
}

for (i in 1:nrow(SenSpez)) {
  x = eval(parse(text = paste0("temp$", names(temp[,i]))))
  SenSpez[i,"Sensitivity"] = sum(x %in% c(-1,1) & temp$CSI_30.30 %in% c(-1,1)) /
                      (sum(x %in% c(-1,1) & temp$CSI_30.30 %in% c(-1,1)) + sum(x == 0 & temp$CSI_30.30 %in% c(-1,1)))
}

for (i in 1:nrow(SenSpez)) {
  x = eval(parse(text = paste0("temp$", names(temp[,i]))))
  SenSpez[i,"Specificity"] = sum(x == 0 & temp$CSI_30.30 == 0) /
                      (sum(x == 0 & temp$CSI_30.30 == 0) + sum(x %in% c(-1,1) & temp$CSI_30.30 == 0))
}

SenSpez$Sensitivity = round(SenSpez$Sensitivity, digits = 3)
SenSpez$Specificity = round(SenSpez$Specificity, digits = 3)

SenSpez %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

Method	n_Changed	n_Unchanged	Total	Sensitivity	Specificity
Mean_PC_30.30	23	77	100	1.000	0.951
RCI_ind_preSD_30.30	37	63	100	0.947	0.765
RCI_ind_pooledSD_30.30	28	72	100	1.000	0.889
EN_30.30	46	54	100	1.000	0.667
CSI_30.30	19	81	100	1.000	1.000
Mean_PC_5.5_Window	28	72	100	0.895	0.864
RCI_ind_preSD_5.5_Window	41	59	100	0.895	0.704
RCI_ind_pooledSD_5.5_Window	29	71	100	0.895	0.852
EN_5.5_Window	47	53	100	1.000	0.654
CSI_5.5_Window	25	75	100	0.842	0.889
Mean_PC_5.5_Days	31	69	100	0.895	0.827
RCI_ind_preSD_5.5_Days	47	53	100	0.895	0.630
RCI_ind_pooledSD_5.5_Days	35	65	100	0.947	0.790
EN_5.5_Days	56	44	100	1.000	0.543
CSI_5.5_Days	25	75	100	0.842	0.889

graphics::barplot(SenSpez$Sensitivity ~ SenSpez$Method, col = "dodgerblue", las = 2, cex.names = 0.7, 
                  main = "Sensitivity to Change (Improvement & Deterioration)")
graphics::barplot(SenSpez$Specificity ~ SenSpez$Method, col = "dodgerblue", las = 2, cex.names = 0.7,
                  main = "Specificity to Change (Improvement & Deterioration)")

Sensitivität & Spezifität gegenüber Verbesserung:
Absolute Häufigkeiten der Veränderungs-Klassifikationen (verbessert vs. nicht verbessert) der Klassifikationsmethoden im Vergleich zur klinischen Signifikanz CSI (je 30 MZP) als “Goldstandard”:

SenSpez = tibble(Method = colnames(temp),
                 n_Improved = as.integer(NA),
                 n_NotImproved = as.integer(NA),
                 Total = as.integer(NA),
                 Sensitivity_Imp = as.numeric(NA),
                 Specificity_Imp = as.numeric(NA))

for (i in 1:nrow(SenSpez)) {
  x = eval(parse(text = paste0("temp$", names(temp[,i]))))
  SenSpez[i,"n_Improved"] = temp %>% summarise(., sum(x == -1)) %>% as.integer()
}

for (i in 1:nrow(SenSpez)) {
  x = eval(parse(text = paste0("temp$", names(temp[,i]))))
  SenSpez[i,"n_NotImproved"] = temp %>% summarise(., sum(x %in% c(-1,1))) %>% as.integer()
}

for (i in 1:nrow(SenSpez)) {
  x = eval(parse(text = paste0("temp$", names(temp[,i]))))
  SenSpez[i,"Total"] = temp %>% summarise(., sum(!is.na(x))) %>% as.integer()
}

for (i in 1:nrow(SenSpez)) {
  x = eval(parse(text = paste0("temp$", names(temp[,i]))))
  SenSpez[i,"Sensitivity_Imp"] = sum(x == -1 & temp$CSI_30.30 == -1) /
                      (sum(x == -1 & temp$CSI_30.30 == -1) + sum(x %in% c(0,1) & temp$CSI_30.30 == -1))
}

for (i in 1:nrow(SenSpez)) {
  x = eval(parse(text = paste0("temp$", names(temp[,i]))))
  SenSpez[i,"Specificity_Imp"] = sum(x %in% c(0,1) & temp$CSI_30.30 %in% c(0,1)) /
                      (sum(x %in% c(0,1) & temp$CSI_30.30 %in% c(0,1)) + sum(x == -1 & temp$CSI_30.30 %in% c(0,1)))
}

SenSpez$Sensitivity_Imp = round(SenSpez$Sensitivity_Imp, digits = 3)
SenSpez$Specificity_Imp = round(SenSpez$Specificity_Imp, digits = 3)

SenSpez %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

Method	n_Improved	n_NotImproved	Total	Sensitivity_Imp	Specificity_Imp
Mean_PC_30.30	23	23	100	1.000	0.951
RCI_ind_preSD_30.30	37	37	100	0.947	0.765
RCI_ind_pooledSD_30.30	28	28	100	1.000	0.889
EN_30.30	46	46	100	1.000	0.667
CSI_30.30	19	19	100	1.000	1.000
Mean_PC_5.5_Window	26	28	100	0.895	0.889
RCI_ind_preSD_5.5_Window	39	41	100	0.895	0.728
RCI_ind_pooledSD_5.5_Window	28	29	100	0.895	0.864
EN_5.5_Window	46	47	100	1.000	0.667
CSI_5.5_Window	24	25	100	0.842	0.901
Mean_PC_5.5_Days	29	31	100	0.895	0.852
RCI_ind_preSD_5.5_Days	45	47	100	0.895	0.654
RCI_ind_pooledSD_5.5_Days	33	35	100	0.947	0.815
EN_5.5_Days	54	56	100	1.000	0.568
CSI_5.5_Days	23	25	100	0.842	0.914

graphics::barplot(SenSpez$Sensitivity_Imp ~ SenSpez$Method, col = "dodgerblue", las = 2, cex.names = 0.7, 
                  main = "Sensitivity to Improvement")
graphics::barplot(SenSpez$Specificity_Imp ~ SenSpez$Method, col = "dodgerblue", las = 2, cex.names = 0.7,
                  main = "Specificity to Improvement")

Sensitivität & Spezifität gegenüber Verschlechterung:
Absolute Häufigkeiten der Veränderungs-Klassifikationen (verschlechtert vs. nicht verschlechtert) der Klassifikationsmethoden im Vergleich zur klinischen Signifikanz CSI (je 30 MZP) als “Goldstandard”:

SenSpez = tibble(Method = colnames(temp),
                 n_Deteriorated = as.integer(NA),
                 n_NotDeteriorated = as.integer(NA),
                 Total = as.integer(NA),
                 Sensitivity_Det = as.numeric(NA),
                 Specificity_Det = as.numeric(NA))

for (i in 1:nrow(SenSpez)) {
  x = eval(parse(text = paste0("temp$", names(temp[,i]))))
  SenSpez[i,"n_Deteriorated"] = temp %>% summarise(., sum(x == 1)) %>% as.integer()
}

for (i in 1:nrow(SenSpez)) {
  x = eval(parse(text = paste0("temp$", names(temp[,i]))))
  SenSpez[i,"n_NotDeteriorated"] = temp %>% summarise(., sum(x %in% c(-1,0))) %>% as.integer()
}

for (i in 1:nrow(SenSpez)) {
  x = eval(parse(text = paste0("temp$", names(temp[,i]))))
  SenSpez[i,"Total"] = temp %>% summarise(., sum(!is.na(x))) %>% as.integer()
}

for (i in 1:nrow(SenSpez)) {
  x = eval(parse(text = paste0("temp$", names(temp[,i]))))
  SenSpez[i,"Sensitivity_Det"] = sum(x == 1 & temp$CSI_30.30 == 1) /
                      (sum(x == 1 & temp$CSI_30.30 == 1) + sum(x %in% c(-1,0) & temp$CSI_30.30 == 1))
}

for (i in 1:nrow(SenSpez)) {
  x = eval(parse(text = paste0("temp$", names(temp[,i]))))
  SenSpez[i,"Specificity_Det"] = sum(x %in% c(-1,0) & temp$CSI_30.30 %in% c(-1,0)) /
                      (sum(x %in% c(-1,0) & temp$CSI_30.30 %in% c(-1,0)) + sum(x == 1 & temp$CSI_30.30 %in% c(-1,0)))
}

SenSpez$Sensitivity_Det = round(SenSpez$Sensitivity_Det, digits = 3)
SenSpez$Specificity_Det = round(SenSpez$Specificity_Det, digits = 3)

SenSpez %>% 
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)

Method	n_Deteriorated	n_NotDeteriorated	Total	Sensitivity_Det	Specificity_Det
Mean_PC_30.30	0	100	100	NaN	1.00
RCI_ind_preSD_30.30	0	100	100	NaN	1.00
RCI_ind_pooledSD_30.30	0	100	100	NaN	1.00
EN_30.30	0	100	100	NaN	1.00
CSI_30.30	0	100	100	NaN	1.00
Mean_PC_5.5_Window	2	98	100	NaN	0.98
RCI_ind_preSD_5.5_Window	2	98	100	NaN	0.98
RCI_ind_pooledSD_5.5_Window	1	99	100	NaN	0.99
EN_5.5_Window	1	99	100	NaN	0.99
CSI_5.5_Window	1	99	100	NaN	0.99
Mean_PC_5.5_Days	2	98	100	NaN	0.98
RCI_ind_preSD_5.5_Days	2	98	100	NaN	0.98
RCI_ind_pooledSD_5.5_Days	2	98	100	NaN	0.98
EN_5.5_Days	2	98	100	NaN	0.98
CSI_5.5_Days	2	98	100	NaN	0.98

#graphics::barplot(SenSpez$Sensitivity_Det ~ SenSpez$Method, col = "dodgerblue", las = 2, cex.names = 0.7, 
#                  main = "Sensitivity to Deterioration")
graphics::barplot(SenSpez$Specificity_Det ~ SenSpez$Method, col = "dodgerblue", las = 2, cex.names = 0.7,
                  main = "Specificity to Deterioration")

1.16 Jackknife-Methode zum Resampling von Messzeitpunkten

Statt wenige zufällige MZP-Kombinationen zu ziehen und diese dann mit den “wahren” Schätzwerten und Klassifikationen (= berechnet anhand der gesamten Intervalle mit je 30 MZP) zu vergleichen, sollen die empirische Verteilung der Parameter und somit der Schätzfehler über Resampling-Methoden wie Jackknife-Verfahren und Bootstrapping berechnet werden.

Percentage Change (PC)

###### EMA_30.30
n = 30

Mean_PC = function(x, ID_df) {(1-((mean(ID_df[x,2])) / (mean(ID_df[x,1])))) * 100}

for (i in 1:nrow(EMA_30.30)) {
  df = data.frame(PRE = as.numeric(EMA_30.30[i,pre_30mzp]), POST = as.numeric(EMA_30.30[i,post_30mzp]))
  
  EMA_30.30[i,"Mean_PC_jse"] = jackknife(1:n, Mean_PC, df)$jack.se
  EMA_30.30[i,"Mean_PC_jbias"] = jackknife(1:n, Mean_PC, df)$jack.bias
  message(i)
}

EMA_30.30_Mean_PC_JK = EMA_30.30 %>% 
  select(ID, Mean_PC_jse, Mean_PC_jbias)
save(EMA_30.30_Mean_PC_JK, file = "Jackknife/EMA_30.30_Mean_PC_JK_k20_n100.RData")

###### EMA_5.5_Window
n = 5

Mean_PC = function(x, ID_df) {(1-((mean(ID_df[x,2])) / (mean(ID_df[x,1])))) * 100}

for (i in 1:nrow(EMA_5.5_Window)) {
  df = data.frame(PRE = as.numeric(EMA_5.5_Window[i,pre_5mzp]), POST = as.numeric(EMA_5.5_Window[i,post_5mzp]))
  
  EMA_5.5_Window[i,"Mean_PC_jse"] = jackknife(1:n, Mean_PC, df)$jack.se
  EMA_5.5_Window[i,"Mean_PC_jbias"] = jackknife(1:n, Mean_PC, df)$jack.bias
  message(i)
}

EMA_5.5_Window_Mean_PC_JK = EMA_5.5_Window %>% 
  select(ID, Mean_PC_jse, Mean_PC_jbias)
save(EMA_5.5_Window_Mean_PC_JK, file = "Jackknife/EMA_5.5_Window_Mean_PC_JK_k20_n100.RData")

###### EMA_5.5_Days
n = 5

Mean_PC = function(x, ID_df) {(1-((mean(ID_df[x,2])) / (mean(ID_df[x,1])))) * 100}

for (i in 1:nrow(EMA_5.5_Days)) {
  df = data.frame(PRE = as.numeric(EMA_5.5_Days[i,pre_5mzp]), POST = as.numeric(EMA_5.5_Days[i,post_5mzp]))
  
  EMA_5.5_Days[i,"Mean_PC_jse"] = jackknife(1:n, Mean_PC, df)$jack.se
  EMA_5.5_Days[i,"Mean_PC_jbias"] = jackknife(1:n, Mean_PC, df)$jack.bias
  message(i)
}

EMA_5.5_Days_Mean_PC_JK = EMA_5.5_Days %>% 
  select(ID, Mean_PC_jse, Mean_PC_jbias)
save(EMA_5.5_Days_Mean_PC_JK, file = "Jackknife/EMA_5.5_Days_Mean_PC_JK_k20_n100.RData")

load("Jackknife/EMA_30.30_Mean_PC_JK_k20_n100.RData")
load("Jackknife/EMA_5.5_Window_Mean_PC_JK_k20_n100.RData")
load("Jackknife/EMA_5.5_Days_Mean_PC_JK_k20_n100.RData")

EMA_30.30 = full_join(EMA_30.30, EMA_30.30_Mean_PC_JK, by = "ID")
EMA_5.5_Window = full_join(EMA_5.5_Window, EMA_5.5_Window_Mean_PC_JK, by = "ID")
EMA_5.5_Days = full_join(EMA_5.5_Days, EMA_5.5_Days_Mean_PC_JK, by = "ID")

temp = tibble(Jackknife_SE = c(EMA_30.30$Mean_PC_jse, EMA_5.5_Window$Mean_PC_jse, EMA_5.5_Days$Mean_PC_jse),
              Datasets = rep(c("EMA_30.30", "EMA_5.5_Window", "EMA_5.5_Days"), each = length(EMA_30.30$Mean_PC_jse)))

temp %>%
  ggplot(aes(x = Jackknife_SE, fill = Datasets)) +
    geom_histogram(alpha = 0.2, binwidth = 1, position = "identity") +
    labs(x = "Jackknife SE of Mean Percentage Change", y = "Cases")

#ggplot(temp, aes(x = Datasets, y = Jackknife_SE)) + 
#  geom_boxplot(na.rm = TRUE) + 
#  ggtitle("Jackknife SEs") +
#  xlab("Dataset")


temp = tibble(Jackknife_Bias = c(EMA_30.30$Mean_PC_jbias, EMA_5.5_Window$Mean_PC_jbias, EMA_5.5_Days$Mean_PC_jbias),
              Datasets = rep(c("EMA_30.30", "EMA_5.5_Window", "EMA_5.5_Days"), each = length(EMA_30.30$Mean_PC_jbias)))

temp %>%
  ggplot(aes(x = Jackknife_Bias, fill = Datasets)) +
    geom_histogram(alpha = 0.2, binwidth = 1, position = "identity") +
    labs(x = "Jackknife Bias of Mean Percentage Change", y = "Cases")

#ggplot(temp, aes(x = Datasets, y = Jackknife_Bias)) + 
#  geom_boxplot(na.rm = TRUE) + 
#  ggtitle("Jackknife Biases") +
#  xlab("Dataset")

RCI(ind) nur mit SD aus dem individuellen Pre-Intervall

###### EMA_30.30
n = 30

RCI_ind_preSD = function(x, ID_df) {(mean(ID_df[x,2]) - mean(ID_df[x,1])) / 
    sqrt(2 * (sd(ID_df[x,1]) * sqrt(1 - EMA_5.5_Alpha))^2)}

for (i in 1:nrow(EMA_30.30)) {
  df = data.frame(PRE = as.numeric(EMA_30.30[i,pre_30mzp]), POST = as.numeric(EMA_30.30[i,post_30mzp]))
  
  EMA_30.30[i,"RCI_ind_preSD_jse"] = jackknife(1:n, RCI_ind_preSD, df)$jack.se
  EMA_30.30[i,"RCI_ind_preSD_jbias"] = jackknife(1:n, RCI_ind_preSD, df)$jack.bias
  message(i)
}

EMA_30.30_RCI_ind_preSD_JK = EMA_30.30 %>% 
  select(ID, RCI_ind_preSD_jse, RCI_ind_preSD_jbias)
save(EMA_30.30_RCI_ind_preSD_JK, file = "Jackknife/EMA_30.30_RCI_ind_preSD_JK_k20_n100.RData")

###### EMA_5.5_Window
n = 5

RCI_ind_preSD = function(x, ID_df) {(mean(ID_df[x,2]) - mean(ID_df[x,1])) / 
    sqrt(2 * (sd(ID_df[x,1]) * sqrt(1 - EMA_5.5_Alpha))^2)}

for (i in 1:nrow(EMA_5.5_Window)) {
  df = data.frame(PRE = as.numeric(EMA_5.5_Window[i,pre_5mzp]), POST = as.numeric(EMA_5.5_Window[i,post_5mzp]))
  
  EMA_5.5_Window[i,"RCI_ind_preSD_jse"] = jackknife(1:n, RCI_ind_preSD, df)$jack.se
  EMA_5.5_Window[i,"RCI_ind_preSD_jbias"] = jackknife(1:n, RCI_ind_preSD, df)$jack.bias
  message(i)
}

EMA_5.5_Window_RCI_ind_preSD_JK = EMA_5.5_Window %>% 
  select(ID, RCI_ind_preSD_jse, RCI_ind_preSD_jbias)
save(EMA_5.5_Window_RCI_ind_preSD_JK, file = "Jackknife/EMA_5.5_Window_RCI_ind_preSD_JK_k20_n100.RData")

###### EMA_5.5_Days
n = 5

RCI_ind_preSD = function(x, ID_df) {(mean(ID_df[x,2]) - mean(ID_df[x,1])) / 
    sqrt(2 * (sd(ID_df[x,1]) * sqrt(1 - EMA_5.5_Alpha))^2)}

for (i in 1:nrow(EMA_5.5_Days)) {
  df = data.frame(PRE = as.numeric(EMA_5.5_Days[i,pre_5mzp]), POST = as.numeric(EMA_5.5_Days[i,post_5mzp]))
  
  EMA_5.5_Days[i,"RCI_ind_preSD_jse"] = jackknife(1:n, RCI_ind_preSD, df)$jack.se
  EMA_5.5_Days[i,"RCI_ind_preSD_jbias"] = jackknife(1:n, RCI_ind_preSD, df)$jack.bias
  message(i)
}

EMA_5.5_Days_RCI_ind_preSD_JK = EMA_5.5_Days %>% 
  select(ID, RCI_ind_preSD_jse, RCI_ind_preSD_jbias)
save(EMA_5.5_Days_RCI_ind_preSD_JK, file = "Jackknife/EMA_5.5_Days_RCI_ind_preSD_JK_k20_n100.RData")

load("Jackknife/EMA_30.30_RCI_ind_preSD_JK_k20_n100.RData")
load("Jackknife/EMA_5.5_Window_RCI_ind_preSD_JK_k20_n100.RData")
load("Jackknife/EMA_5.5_Days_RCI_ind_preSD_JK_k20_n100.RData")

EMA_30.30 = full_join(EMA_30.30, EMA_30.30_RCI_ind_preSD_JK, by = "ID")
EMA_5.5_Window = full_join(EMA_5.5_Window, EMA_5.5_Window_RCI_ind_preSD_JK, by = "ID")
EMA_5.5_Days = full_join(EMA_5.5_Days, EMA_5.5_Days_RCI_ind_preSD_JK, by = "ID")

temp = tibble(Jackknife_SE = c(EMA_30.30$RCI_ind_preSD_jse, EMA_5.5_Window$RCI_ind_preSD_jse, EMA_5.5_Days$RCI_ind_preSD_jse),
              Datasets = rep(c("EMA_30.30", "EMA_5.5_Window", "EMA_5.5_Days"), each = length(EMA_30.30$RCI_ind_preSD_jse)))

temp %>%
  ggplot(aes(x = Jackknife_SE, fill = Datasets)) +
    geom_histogram(alpha = 0.2, binwidth = 1, position = "identity") +
    labs(x = "Jackknife SE of RCI(ind) With Pre-SDs", y = "Cases")

#ggplot(temp, aes(x = Datasets, y = Jackknife_SE)) + 
#  geom_boxplot(na.rm = TRUE) + 
#  ggtitle("Jackknife SEs") +
#  xlab("Dataset")


temp = tibble(Jackknife_Bias = c(EMA_30.30$RCI_ind_preSD_jbias, EMA_5.5_Window$RCI_ind_preSD_jbias,
                                 EMA_5.5_Days$RCI_ind_preSD_jbias),
              Datasets = rep(c("EMA_30.30", "EMA_5.5_Window", "EMA_5.5_Days"), each = length(EMA_30.30$RCI_ind_preSD_jbias)))

temp %>%
  ggplot(aes(x = Jackknife_Bias, fill = Datasets)) +
    geom_histogram(alpha = 0.2, binwidth = 1, position = "identity") +
    labs(x = "Jackknife Bias of RCI(ind) With Pre-SDs", y = "Cases")

#ggplot(temp, aes(x = Datasets, y = Jackknife_Bias)) + 
#  geom_boxplot(na.rm = TRUE) + 
#  ggtitle("Jackknife Biases") +
#  xlab("Dataset")

RCI(ind) mit pooled SDs aus beiden individuellen Intervallen

###### EMA_30.30
n = 30

RCI_ind_pooledSD = function(x, ID_df) {(mean(ID_df[x,2]) - mean(ID_df[x,1])) / 
    sqrt((sd(ID_df[x,1])^ 2 + sd(ID_df[x,2])^ 2) * (1 - EMA_5.5_Alpha))}

for (i in 1:nrow(EMA_30.30)) {
  df = data.frame(PRE = as.numeric(EMA_30.30[i,pre_30mzp]), POST = as.numeric(EMA_30.30[i,post_30mzp]))
  
  EMA_30.30[i,"RCI_ind_pooledSD_jse"] = jackknife(1:n, RCI_ind_pooledSD, df)$jack.se
  EMA_30.30[i,"RCI_ind_pooledSD_jbias"] = jackknife(1:n, RCI_ind_pooledSD, df)$jack.bias
  message(i)
}

EMA_30.30_RCI_ind_pooledSD_JK = EMA_30.30 %>% 
  select(ID, RCI_ind_pooledSD_jse, RCI_ind_pooledSD_jbias)
save(EMA_30.30_RCI_ind_pooledSD_JK, file = "Jackknife/EMA_30.30_RCI_ind_pooledSD_JK_k20_n100.RData")

###### EMA_5.5_Window
n = 5

RCI_ind_pooledSD = function(x, ID_df) {(mean(ID_df[x,2]) - mean(ID_df[x,1])) / 
    sqrt((sd(ID_df[x,1])^ 2 + sd(ID_df[x,2])^ 2) * (1 - EMA_5.5_Alpha))}

for (i in 1:nrow(EMA_5.5_Window)) {
  df = data.frame(PRE = as.numeric(EMA_5.5_Window[i,pre_5mzp]), POST = as.numeric(EMA_5.5_Window[i,post_5mzp]))
  
  EMA_5.5_Window[i,"RCI_ind_pooledSD_jse"] = jackknife(1:n, RCI_ind_pooledSD, df)$jack.se
  EMA_5.5_Window[i,"RCI_ind_pooledSD_jbias"] = jackknife(1:n, RCI_ind_pooledSD, df)$jack.bias
  message(i)
}

EMA_5.5_Window_RCI_ind_pooledSD_JK = EMA_5.5_Window %>% 
  select(ID, RCI_ind_pooledSD_jse, RCI_ind_pooledSD_jbias)
save(EMA_5.5_Window_RCI_ind_pooledSD_JK, file = "Jackknife/EMA_5.5_Window_RCI_ind_pooledSD_JK_k20_n100.RData")

###### EMA_5.5_Days
n = 5

RCI_ind_pooledSD = function(x, ID_df) {(mean(ID_df[x,2]) - mean(ID_df[x,1])) / 
    sqrt((sd(ID_df[x,1])^ 2 + sd(ID_df[x,2])^ 2) * (1 - EMA_5.5_Alpha))}

for (i in 1:nrow(EMA_5.5_Days)) {
  df = data.frame(PRE = as.numeric(EMA_5.5_Days[i,pre_5mzp]), POST = as.numeric(EMA_5.5_Days[i,post_5mzp]))
  
  EMA_5.5_Days[i,"RCI_ind_pooledSD_jse"] = jackknife(1:n, RCI_ind_pooledSD, df)$jack.se
  EMA_5.5_Days[i,"RCI_ind_pooledSD_jbias"] = jackknife(1:n, RCI_ind_pooledSD, df)$jack.bias
  message(i)
}

EMA_5.5_Days_RCI_ind_pooledSD_JK = EMA_5.5_Days %>% 
  select(ID, RCI_ind_pooledSD_jse, RCI_ind_pooledSD_jbias)
save(EMA_5.5_Days_RCI_ind_pooledSD_JK, file = "Jackknife/EMA_5.5_Days_RCI_ind_pooledSD_JK_k20_n100.RData")

load("Jackknife/EMA_30.30_RCI_ind_pooledSD_JK_k20_n100.RData")
load("Jackknife/EMA_5.5_Window_RCI_ind_pooledSD_JK_k20_n100.RData")
load("Jackknife/EMA_5.5_Days_RCI_ind_pooledSD_JK_k20_n100.RData")

EMA_30.30 = full_join(EMA_30.30, EMA_30.30_RCI_ind_pooledSD_JK, by = "ID")
EMA_5.5_Window = full_join(EMA_5.5_Window, EMA_5.5_Window_RCI_ind_pooledSD_JK, by = "ID")
EMA_5.5_Days = full_join(EMA_5.5_Days, EMA_5.5_Days_RCI_ind_pooledSD_JK, by = "ID")

temp = tibble(Jackknife_SE = c(EMA_30.30$RCI_ind_pooledSD_jse, EMA_5.5_Window$RCI_ind_pooledSD_jse,
                               EMA_5.5_Days$RCI_ind_pooledSD_jse),
              Datasets = rep(c("EMA_30.30", "EMA_5.5_Window", "EMA_5.5_Days"), each = length(EMA_30.30$RCI_ind_pooledSD_jse)))

temp %>%
  ggplot(aes(x = Jackknife_SE, fill = Datasets)) +
    geom_histogram(alpha = 0.2, binwidth = 1, position = "identity") +
    labs(x = "Jackknife SE of RCI(ind) With Pooled SDs", y = "Cases")

#ggplot(temp, aes(x = Datasets, y = Jackknife_SE)) + 
#  geom_boxplot(na.rm = TRUE) + 
#  ggtitle("Jackknife SEs") +
#  xlab("Dataset")


temp = tibble(Jackknife_Bias = c(EMA_30.30$RCI_ind_pooledSD_jbias, EMA_5.5_Window$RCI_ind_pooledSD_jbias,
                               EMA_5.5_Days$RCI_ind_pooledSD_jbias),
              Datasets = rep(c("EMA_30.30", "EMA_5.5_Window", "EMA_5.5_Days"), each = length(EMA_30.30$RCI_ind_pooledSD_jbias)))

temp %>%
  ggplot(aes(x = Jackknife_Bias, fill = Datasets)) +
    geom_histogram(alpha = 0.2, binwidth = 1, position = "identity") +
    labs(x = "Jackknife Bias of RCI(ind) With Pooled SDs", y = "Cases")

#ggplot(temp, aes(x = Datasets, y = Jackknife_Bias)) + 
#  geom_boxplot(na.rm = TRUE) + 
#  ggtitle("Jackknife Biases") +
#  xlab("Dataset")

EMA-Stichprobenvergleiche (d = 0.88) für n = 100

Stephan Bartholdy

30 Oktober 2020

1 Vergleich von Klassifikationsmethoden in simulierten EMA-Daten

1.1 Drawing a Random Sample of n = 100

1.2 Überblick über die simulierten Daten

1.2.1 Original-Simulationsdaten (je 5 MZP)

1.2.2 Erweiterte Intervall-Daten (je 30 MZP)

1.2.3 Zufallsauswahl: Random Window (je 5 MZP)

1.2.4 Zufallsauswahl: Random Days (je 5 MZP)

1.3 Deskriptive Statistiken der Datensets

1.4 Reliabilitäten und Inter-Item-Korrelationen

1.4.1 EMA_5.5 (je 5 MZP)

1.4.2 EMA_30.30 (je 30 MZP)

1.4.3 EMA_5.5_Window (je 5 MZP)

1.4.4 EMA_5.5_Days (je 5 MZP)

1.5 Pre-Post-Differenz

1.5.1 Cohen´s d

1.6 Klinische PHQ-9-Interpretation

1.6.1 EMA_30.30

1.6.2 EMA_5.5_Window

1.6.3 EMA_5.5_Days

1.7 Percentage Change (PC)

1.7.1 EMA_30.30

1.7.2 EMA_5.5_Window

1.7.3 EMA_5.5_Days

1.7.4 Zusammenhang im Scatter-Histogramm

1.8 Individual Reliable Change Index (ind)

1.8.1 RCI(ind) nur mit SD aus dem individuellen Pre-Intervall

1.8.2 RCI(ind) mit pooled SD aus beiden individuellen Intervallen

1.9 Vergleich RCI(ind) (nur Pre-SD) - RCI(ind) (pooled SDs)

1.10 RCI-Klassifikationen

1.11 Edwards-Nunnally-Methode (EN) nach Speer (1992)

1.12 Clinically Significant Improvement (CSI)

1.12.1 CSI in EMA_30.30

1.12.2 CSI in EMA_5.5_Window

1.12.3 CSI in EMA_5.5_Days

1.13 Sudden Gains

1.13.1 Sudden Gains/Losses in EMA_30.30

1.13.2 Sudden Gains/Losses in EMA_5.5_Window

1.13.3 Sudden Gains/Losses in EMA_5.5_Days

1.14 Individuelle Übereinstimmung der Klassifikationen

1.14.1 Klinische PHQ-9-Interpretation

1.14.2 Zusammenfassung der Klassifikations-Häufigkeiten

Data Frame Summary

temp

1.14.3 Übereinstimmung der Klassifikations-Häufigkeiten

1.15 Sensitivität und Spezifität der Klassifikationsmethoden

1.16 Jackknife-Methode zum Resampling von Messzeitpunkten